Although he has been ill for several days, Lars Nittve has risen from his sickbed to make our interview. Flu, I presume, but he says mysteriously: "No, something a bit more serious. But I am having the antibiotics, and the temperature has gone away." This is good news, particularly given that, in the arena of millennial cultural projects, hopeful prognoses are in such short supply. The combination of maladies strangling the Dome never did respond to treatment. The blancmange syndrome afflicting Sir Norman Foster's bridge has proved chronic. However frail its director is currently feeling, only Tate Modern has looked healthy from the start.
Next week is the first anniversary of the museum's opening. It was expected that, in the initial year, 2.5 million would visit Jacques Herzog's and Pierre de Meuron's conversion of the old Bankside power station designed by Sir Giles Gilbert Scott. Nittve now expects the final tally to be more than double that, at 5.3 million. Tate Modern, a retro-industrial cavern, has become the cultural honey pot of the swarming classes in search of the Brobdingnagian experience. Disney for thrills, Bluewater for browsing, IKEA for sofas and queue-induced nervous breakdowns, Bankside for art. So vast are the crowds that Nittve, though an admirer of Foster's "beautiful miracle of a bridge", is rather relieved that it proved such a turkey. "In terms of visitor numbers, we should be happy that it didn't open the first year. We have been just on the edge of the numbers we could handle. A million more people could have been a disaster for us - unbearable."
Being ringmaster of the hottest circus in town does not seem to have unduly excited Nittve. An imperturbable man of 47, he is divorced with an 11-year-old son, who has visited every third weekend since his father was hired by the Tate director, Sir Nicholas Serota. Formerly a major curator and art critic in Sweden and Denmark, Nittve started out as a librarian, worked as a ski instructor and was halfway through an economics degree in Stockholm when he switched to history of art. His political development is a more gradualist curve from schoolboy Maoism to the "social liberalism" that informs, among much else, Tate Modern's cafeteria set-up.
Pricey restaurants with panoramic vistas over the Thames are out. High-rise cheese-and-pickle baps are in. As Nittve says: "There shouldn't be a hierarchy between views. You should be able to have a cheap sandwich on the higher floors, rather than a gourmet meal. The commercial instinct is an upstairs/downstairs arrangement, but it should be democratic.
"The only hierarchy is that the higher you go, the longer you queue." Ambitious high-rollers in the contemporary art world may reflect that this precept also applies to them. When Nittve was appointed in preference to home-grown contenders for the biggest new arts job on offer in Britain for years, he joined a string of influential incomers. His compatriot Sven-Goran Eriksson coaches the England football team. In the arts, Karsten Witt (Austrian) runs the South Bank and Michael Kaiser (American) has recently left as chief executive of the Royal Opera House. Although Pierre-Yves Gerbeau could not save the Dome, he did invest it with some verve, and Bob Kiley (American) might yet save the Tube, if only the government would let him. Why do we have to import so much talent?
"Maybe I had more international experience than most in Britain. Because Sweden is a small country, you tend to work outside your turf," he says tactfully. "Ultimately, when you come to this level of job, in a corporation or a gallery - it's about the individual rather than the nationality. Nationality doesn't really matter any more." Besides, globalisation cuts both ways. His counterpart in Stockholm, until recently, was a Briton.
Only two aspects of British cultural life astound Nittve. The first is sex; the second is money. I ask what he made of the uproar surrounding the Saatchi Gallery's recent display of photos of nude children, and he says: "That sort of thing has surprised me more than anything else here. It shocked me totally. I don't mean that one shouldn't have an awareness of paedophilia and exploitation, but it should take a lot before one censors or even thinks about censoring an artwork."
British prudishness so alarmed him that he took legal advice before agreeing to hang Egon Schiele's dark depictions of masturbating children as part of Tate Modern's "Century City" exhibition, which has just ended. "There were no complaints that I heard of, but we did put up warnings before people entered the Vienna section." Does he think that Charles Saatchi, whose latest show includes a more anodyne depiction of masturbation, is a fighter for freedom or a man with an eye for a publicity stunt? "He would be stupid if he didn't try to trigger some media coverage. He knows this game better than anyone."
A fast learner, Nittve is not yet so slick. He seems not quite to see that he is publicly perceived as the luckiest of curators, presiding over a gilded showcase awash with government money. In the regions, museums are starved of cash, and local arts boards, threatened with extinction, rail against the Arts Council's "moronic plans". While Nittve is not unsympathetic to out-of-towners, he seems to think his plight is as bad, if not far worse. Government stinginess, he claims, is severely restricting Tate Modern's dreams.
"Our grant-in-aid is £5m. That happens to work out at £1 per visitor this year. We're quite a cheap museum, and we are pretty badly underfunded." By how much? "I need another £2m. That would give us the opportunity of a much richer programme, involving smaller projects and a dialogue with the community - things that give life and texture and make us less of a colossus. Now we can do just six large exhibitions a year, and that's it. A normal, charging museum of modern art in Europe has between 60 and 80 per cent of their running costs met by government. We have 40 to 45 per cent, and we're not charging. I think the government is very aware that we want more money. I hope it is listening."
Nittve is a supporter of free entry to galleries, but he feels himself the poor relation to his vastly richer rivals, such as the Museum of Modern Art in New York and the Centre Pompidou in Paris. Although he admires Chris Smith, he has never met Tony Blair or been invited to Downing Street, which he seems to think quite odd. Does he concur with the Drummond-Tusa-Naipaul axis who view Blair as a philistine?
"Actually, I don't know whether the government has a deep understanding of the arts or not. Personal drivers are not important to me. Policies are. I was hoping, especially given our success, that we would get fuller support from this government . . . It's a challenge to do things in a lean way. That is very nice up to a point, but if we had more resources it would benefit the public."
According to the few critics of Tate Modern, a change of approach might also help. Some, such as Jed Perl, think the museum a "fraud", a ghastly funhouse with the "numbingly over- scaled . . . proportions of a fascist nightmare". Others find the thematic organisation of the galleries (a Monet here, a Richard Long there) trite and tendentious. Nittve's wish to eschew a parade of canonical masterpieces (of which he has few) in favour of a social statement has been abhorred by those critics who sense a patronising con on an ignorant public.
Naturally, Nittve disagrees. "When we started out, we had to counter what is an international tendency to become a theme park. We had to be rigorous about what we show and why it is together. The [Bilbao] Guggenheim is so much more about the building than the gallery space, while Tate Modern gives artists close to their dream spaces. I don't accept the criticism." Although he classifies his opposition as the "Brian Sewells of the world", others denounced the "Century City" exhibition as "an appalling start" and a "joyless stew".
Even Nittve admits now that its execution was flawed. "We were trying to do something that could hardly be judged as an exhibition. It was a new genre, and we didn't manage to communicate that to the British visitor - that you should spend a whole day or come back twice." What, at £8.50 a go? "We're not the market leader when it comes to prices," he argues. "It's not much compared with what the Royal Academy charges for its larger exhibitions, and they are smaller than ours." But does size matter to a British public for whom a glut of Monet waterlilies may be the visual equivalent of well-done steak and chips. Are we a nation of cultural morons?
There is a long pause before Nittve says, with careful tact: "I don't think there is a major difference from elsewhere, although I know that is the view here. I am often asked questions about the philistinism of the British public. I don't think there is a particular extreme here. We only have this one museum of modern art, so people are not as used to seeing contemporary art as they are in other cities." So Nittve's mission is to teach them. Critics who condemn his efforts are dismissed as "those who want to protect high art from the masses", but he, too, is protective. His visitors must be informed, welcomed and shielded from rip-off catering. Even the "Do Not Touch" notices are hedged with polite qualifiers.
Nittve does seem to be on the punters' side. Though he mentions the prestige projects to come (sculptures by Juan Munoz in the turbine hall, Arte Povera and, in the autumn, the capital's first major surrealist exhibition for 20 years), he seems almost more fired up by the small stuff. Part missionary, part social worker, he wants to "create a major big institution that doesn't feel like an alien spaceship that has landed in the community". He, I imagine, will not be so seamlessly integrated into established ways. A less outsiderish director than Nittve might, for example, hint that Tate Modern is a symbol of the innovative brilliance of this government rather than evidence of its penny-pinching ways.