In his final visit to Moscow as president, Bill Clinton arrived here today and dined tonight with Russia's new president, Vladimir V. Putin, at the Kremlin palace, where the two leaders made a ''very serious and focused beginning'' on a full range of issues, including the search for a compromise on antimissile defense.

During a nearly three-hour working dinner, the two men also discussed the American-Russian nuclear relationship, ongoing conflicts in the Balkans and the Caucasus, international trade and the state of the Russian economy, said a senior Administration official who sat in on the talks.

The official described the talks as ''businesslike,'' ''congenial'' and ''easygoing.''

''Businesslike is good; businesslike is good,'' the official said, putting a positive cast on the talks, but declining to discuss them except in the vaguest terms. ''Remember that the two presidents do know each other, and that was quite apparent from the beginning.''

Mr. Clinton met Mr. Putin twice last year when he was prime minister, once at a tribute in Oslo to the late Israeli prime minister Yitzhak Rabin and a second time at the annual economic summit of Pacific Rim countries, but the talks that started today and will continue through Sunday represent their first face-to-face encounter since Mr. Putin was elected president in March.

During their talks, Mr. Putin spoke some English and both leaders showed an enthusiasm to hear out the other's position on items of dispute, the administration official said. But he acknowledged that the initial exchanges lacked the first-name familiarity that characterized the relationship between Mr. Clinton and Russia's last president, Boris N. Yeltsin, where it was always Boris and Bill.

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After a dinner of cold boiled boar, baked ham and cabbage and goose with berry sauce, Mr. Putin led Mr. Clinton on a tour of the residence, showing him a personal study, a small chapel, a gym and a massage room. The leaders settled into armchairs in an intimate wood-paneled theater for a jazz tribute to Louis Armstrong, conducted by one of Russia's best-known band leaders, Oleg Lundsrem.

Mr. Clinton has arrived to find Mr. Putin absorbed with domestic politics, a wrenching set of economic reforms just getting under way and an unresolved war in Chechnya.

At the same time, Mr. Clinton has come to a Russia that is relatively stable, poised for economic recovery and more politically united -- though disputes abound -- than at any time since the collapse of the Soviet Union in 1991.

This is a sharp contrast with Mr. Clinton's most recent visits here -- in 1996 when former President Yeltsin was fighting for his political life against an entrenched Communist opposition, and in 1998 when the Russian ruble and much of the country's economy had collapsed.

Like a younger Bill Clinton eight years ago (Mr. Clinton was 46 when he entered office; Mr. Putin is 47), Mr. Putin has taken command of the Kremlin with an apparent determination to focus on his country's economic problems and other pressing domestic issues while keeping things quiet on the foreign policy front. There, America still looms as an enormous force in Russia's calculations on everything from financial assistance and debt restructuring to NATO expansion and arms control.

Mr. Clinton is seeking agreement to modify a 1972 treaty and thus go ahead with a national antimissile defense; Russia has so far refused.

Right after his inauguration last month, Mr. Putin, a former K.G.B. officer, stirred liberal fears about his commitment to democracy when heavily armed police raided the offices of a top news media organization. On Sunday, Mr. Clinton will sit for a radio interview -- with live questions from the audience over the Internet -- on the popular Ekho Moskvy station run by the media group in what is intended as a gesture of support for freedom of the press in Russia.

On Monday, Mr. Clinton will address the Russian Duma, or lower house of Parliament, which has formed a strong pro-reform, and pro-Putin majority since elections last December, though many battles over land ownership, regional autonomy and national investment lie ahead.

The economic reality that Russia faces was highlighted most glaringly by Mr. Putin himself after he was named acting president on New Year's Eve when Mr. Yeltsin resigned.

''To reach the production level of Portugal and Spain, two countries that are not known as leaders of the world economy,'' Mr. Putin said, ''it will take Russia approximately 15 years'' even under optimistic growth assumptions of 8 percent a year. Only twice in the 20th century, he said, had Russia been so weak, ''after the October Revolution in 1917, and in the 1990's.''

Mr. Putin, as a political unknown whose disposition to the Western eye is somewhat dour, seems unlikely to achieve with Mr. Clinton the easy-going ''Boris and Bill'' chemistry that dominated during Mr. Yeltsin's two terms.

Under Mr. Putin, still very much the man in the gray suit, a more pragmatic and businesslike style prevails these days in the Kremlin, though he has bonded in an openly friendly manner with Prime Minister Tony Blair of Britain.

And Mr. Putin has betrayed a certain admiration for Mr. Clinton. When the two leaders met last fall in New Zealand at a meeting of Asian-Pacific leaders, Mr. Putin was still a novice prime minister, whose popularity among Russians was soaring due to his resolute prosecution of the war in Chechnya. Mr. Putin admitted to a group of interviewers from the newspaper Kommersant that he was charmed by Mr. Clinton.

''In that first meeting, he paid special attention to me,'' Mr. Putin said, referring to Mr. Clinton. ''He made a point of coming up to me. We had been seated at different tables. We talked about something for a while, and then he said, 'Well, shall we go?' All the heads of state lined up. And he and I walked together along that corridor. We exited the hall to the sound of applause. I appreciated this sign of special regard,'' Mr. Putin said.

While clearly Mr. Putin has strong views, especially on NATO expansion and on the restoration of Russian power and national dignity in international affairs, he has shown great pragmatism in avoiding confrontation with the West, where he says he sees Russia's future as a European nation.

Mr. Clinton adopted that theme on Friday, when he used a speech accepting a prestigious European award to appeal to western Europeans to admit Russia, eventually, to both NATO and the European Union.

One of the problems facing Mr. Clinton is that both leaders know that history has assigned them different time slots in different decades. Mr. Clinton is almost at the end of his term and Mr. Putin is just embarking on his. And this difference in phase may do more to define the psychology at this summit meeting than any other factor.

Mr. Clinton has come here seeking to make progress on his proposal to build a system of national missile defense that requires an agreement to amend the treaty banning such nationwide systems signed by Moscow and Washington more than 30 years ago.

If accepted by Russia, the American proposal represents a profound turning point from offensive to defensive strategies by the world's two largest nuclear powers, one with the potential to reignite an arms race and alienate China, whose small nuclear arsenal would loose its deterrent credibility. Mr. Putin sent his foreign minister to New York last month to warn at the United Nations that America's missile defense plans could destabilize three decades of arms control agreements.

However, in an interview just before Mr. Clinton's arrival with ''The NBC Nightly News,'' Mr. Putin hinted that the United States and Russia might collaborate on new ways to shoot down enemy missiles soon after they were launched, and thus address the problems posed by nuclear weapons being acquired by so-called rogue states. Mr. Clinton says the United States seeks an antimissile defense only to address that threat, although the Russians and Chinese are skeptical that this is the true purpose.

Although Mr. Putin will certainly engage Mr. Clinton's arguments, the Russian leader knows that he also has the luxury to wait for the next American president. That gives him an advantage over Mr. Clinton, who is in a hurry to improve the final cornice work of his presidency.

On the domestic front, Mr. Putin has opened his term with a strategy to strengthen federal power over Russia's vast region in preparation for slogging economic reforms. He has also has proposed legislation to gut and remake the upper house of Parliament and bolster the independence of the judiciary. His proposals appear so sweeping that his critics have attacked him for trying to recreate the vertical power structure of the Soviet Union.

The Russian leader's personal views on the subject have only deepened those concerns. ''From the very beginning, Russia was created as a supercentralized state,'' he told interviewers this spring. ''That's practically laid down in its genetic code, its traditions and the mentality of its people.''

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