President Clinton warned Russian Prime Minister Vladimir Putin here today that money laundering and other forms of financial corruption purportedly plaguing his country are problems that "could eat the heart out of Russian society."

Clinton was meeting for the first time with President Boris Yeltsin's newest premier, a session that came as long-standing concerns about financial corruption at the top levels of Russian society are flaring anew and U.S. critics are charging that the Clinton administration has based too much of its Russia policy on support for Yeltsin.

Clinton also used the annual Asia-Pacific Economic Cooperation forum to host a three-way meeting with Japanese Prime Minister Keizo Obuchi and South Korean President Kim Dae Jung. Their discussions centered on North Korea, which concluded six days of talks today with U.S. officials in Berlin that were designed to forestall the test-firing of a new long-range missile by the Pyongyang government. Western officials in the German capital said the North Koreans had agreed to what amounts to a freeze in the missile-testing program, a move that clears the way for better relations with the United States and its key Asian allies.

Describing a "carrot-and-stick" set of incentives to a Communist nation that has been isolated for years by strict international sanctions, White House national security adviser Samuel R. "Sandy" Berger said the three leaders "indicated that if there was a manifestation by the North Koreans that they would not proceed with testing, that some form of easing of the sanctions would be appropriate." The Clinton administration is currently reviewing its North Korean policy.

Clinton's vivid language in his meeting with Putin about the perils of government corruption--recounted afterward by Berger--was cited by administration officials as a reflection of how seriously the president regards the problem.

In a telephone conversation last week, the Russian president told Clinton that allegations of corruption involving his family were being spread by his political adversaries. Those allegations, involving purported illicit payments by a Swiss construction company, surfaced last week amid reports that U.S. prosecutors suspect billions of dollars of Russian money may have been laundered through the Bank of New York.

While Putin also cited political scandal-mongering as a source of the allegations, his response, as U.S. officials described it, was somewhat less dismissive than Yeltsin's. "He acknowledged that money-laundering problems exist in Russia," while emphasizing that the problem was not unique to his country, Berger said. Referring to a team of Russian law enforcement officials who will visit Washington this week to talk about money laundering, Putin promised a "cooperative approach in dealing with the problem."

Berger said Putin also struck a noncombative note on other issues over which the two nations have been at odds, including the Clinton administration's efforts to modify an antiballistic missile treaty to allow development of missile defense technologies. Clinton has said that the threat of missiles launched by terrorists or rogue states justifies changes to the treaty, changes that have drawn objections from Russia.

Putin also told Clinton that ratification of the START II nuclear weapons reduction treaty, which U.S. officials have intermittently portrayed as on the verge of passage for several years, remains stalled in the Russian parliament. Berger quoted Putin as saying that "ratification of START II right now would be difficult, but . . . we're trying our best." Putin also said he thinks there is some wavering among opponents of START II, Berger said.

Most nations are represented at the APEC summit by their heads of government, but Yeltsin did not come. Berger said he did not know why but assumed it was "health- and stamina-related." Clinton was pleased with the Putin meeting, Berger said, and pleased too that the new prime minister--who formerly served as the Russian equivalent of national security adviser--may have a much longer tenure than recent predecessors.

"The president felt that he is somebody who has fairly substantial experience in the Russian system and, therefore, perhaps to a greater extent than some of his predecessors may be able to work the system," Berger said.

CAPTION: Yeltsin, shown in Moscow on Friday, sent his premier to the summit.

CAPTION: President Clinton shakes hands with Russian Prime Minister Vladimir Putin before the two held talks during the Asian economic summit in Auckland, New Zealand.