After co-chairing this week's regular session of the US-Russian co-operation commission with Vice-President Al Gore, Mr Chernomyrdin yesterday met President Bill Clinton, promising Moscow would continue on the path of "reform", but warning that "certain corrections" were necessary.
It is these "corrections", however, which concern the administration as it debates whether it should still support Mr Yeltsin. Some advisers take that view, arguing that the sackings of economic reformers from the government, and even the brutal Chechen campaign, were dictated by Mr Yeltsin's need to shore up his position among conservatives before an expected announcement that he will stand for re-election.
Other administration officials insist Mr Yeltsin is simply too erratic, too discredited and unwell, and that Washington ought to throw in its lot with genuine reformers such as Grigory Yavlinksy, candidate of the liberal Yabloko party in the June vote.
The uncertainty has spread to the International Monetary Fund, where problems have unexpectedly arisen with a new $9bn (pounds 6bn) credit line that Moscow has been negotiating to consolidate its move to a market economy.
Yesterday Mr Chernomyrdin held separate talks with the IMF managing director, Michel Camdessus, to iron out the difficulties. According to the Russians these surround the conditions attached to the credit. In fact they have been caused by the lurch away from reform, including delays in privatisation programmes on which the IMF has insisted.
Washington now faces the dilemma it confronted six years ago, as former president Mikhail Gorbachev lost his grip on the dying Soviet Union: whether to stick with a familiar leader (as by common consent it did for too long in the case of Mr Gorbachev), or seek an alternative.
This time, all that US officials agree on is that the most probable alternatives, the Communists under Gennady Zyuganov, or the ultra-nationalist Vladimir Zhirinovsky, would be worse. To complicate matters, they know well that in the current climate in Russia, overt backing for Mr Yeltsin or any other "reformist" would be more of a hindrance than a help.
Hence there is extreme caution on both sides. "The market reforms will continue," Mr Chernomyrdin assured Mr Gore, before adding that the Yeltsin government would be making "some corrections in the social sphere".
The response from the State Department was equally laconic. The Russian Prime Minister's warning was "not ominous in any way", a spokesman said, before refusing to comment on the latest economic policy decisions taken in Moscow.Reuse content