President Bush discussed the turmoil in the Soviet Union during a 30-minute meeting with Soviet Ambassador Alexander Bessmertnykh at the White House yesterday, and said afterward that Moscow had "a determination to keep going down this path of reform" despite the deepening economic and political crisis facing Soviet President Mikhail Gorbachev.

Bessmertnykh brought a New Year's greeting message from Gorbachev to Bush, according to U.S. and Soviet officials. Bush, who returned temporarily to Washington yesterday morning from his holiday vacation at Camp David, said before departing again in the afternoon that they talked about the challenges to Gorbachev's reform program in the wake of the resignation of Foreign Minister Eduard Shevardnadze, and this week's tumultous session of the Congress of People's Deputies.

Bush did not disclose the contents of the message, the first he has received from Gorbachev since Shevardnadze warned last week that the nation was heading toward dictatorship. Gorbachev's recent efforts to reassert authority have prompted concern in the Bush administration that he may be forsaking his economic and political reforms and contemplating a crackdown on rebellious republics.

Separately, administration sources said Bessmertnykh met earlier this week with Undersecretary of State for Political Affairs Robert M. Kimmitt to discuss U.S.-Soviet relations. Kimmitt is serving as acting secretary while James A. Baker III is on vacation.

According to informed sources, Kimmitt wanted to convey to Moscow the desire of the United States to move ahead on a range of still-pending issues that had been the subject of intensive discussion with Shevardnadze.

Those issues include settlement of regional conflicts in Afghanistan and Cambodia and the nearly complete strategic arms reduction treaty. None of the changes discussed by Baker and Shevardnadze have been locked into a final agreement, however, and officials have been concerned that the talks continue to move ahead when Gorbachev picks a new foreign minister.

In addition, Shevardnadze had been a leading advocate in the Soviet leadership for cooperation with the United States and other nations in the alliance against Iraqi President Saddam Hussein. Although U.S. officials said they believed Gorbachev would not retreat from this basic course, they have been concerned that Shevardnadze's departure not create problems for the international effort.

In the Bessmertnykh meeting, Kimmitt was assured that the Soviets also want continuity in their relations with the United States, the sources said.

Bush said he had received "some very friendly words of greeting" from the Soviet president.

"We obviously discussed some of the problems that exist there, but it was just one more in what's become a series of exchanges with the president of the Soviet Union," Bush said. "That's good."

Asked for his assessment of the Soviet leadership changes and other problems, Bush replied, "Well, the reading is that they're having difficulties, economic difficulties principally, difficulties in sorting out this new federation. But any time you move from a totalitarian, totally controlled state, to an open state . . . you're bound to have problems."

Bush also said, "The main thing is there's a determination to keep going down this path of reform, and that's very important. But it's hardly up to me to try to fine-tune the difficulties that they're having there."

Staff writer Dan Balz contributed to this report.