Speaking after a meeting at the World Bank, shortly before his first encounter with Vice President Al Gore, Mr Chernomyrdin insisted the next scheduled summit between Mr Yeltsin and President Bill Clinton would be held in the second half of March. Its location, however, remains uncertain. It is Mr Yeltsin's turn to come to the US, but White House officials say Mr Clinton might agree to travel to Europe, to allow the Russian leader to conserve his strength.
Privately, however, many US officials are doubtful that a meaningful meeting can be held with Mr Yeltsin in his present enfeebled condition, and pessimistic that he will ever regain his former powers. Hence the importance attached to the visit of the Russian premier, a pragmatist who would probably be Washington's choice to take over from Mr Yeltsin at this delicate juncture in Russian affairs.
The hope is that Mr Chernomyrdin's meetings with Mr Gore, and with Mr Clinton at the White House today, will breathe new life into relations between Washington and Moscow. But Nato expansion complicates every calculation, including the timing of a Clinton/Yeltsin summit.
At the White House, Mr Chernomyrdin is likely to spell out Moscow's objections to the eastward expansion of Nato. Privately, the Kremlin accepts enlargement as inevitable, but the Prime Minister will argue that without some gesture to Moscow, the move could have destabilising consequences, both in central and Eastern Europe and within their own country.
Among the hostages to Nato enlargement is the stalled ratification by the Duma (Russian parliament) of the 1993 Start-2 nuclear arms reduction treaty, a deadlock which Washington might try to leapfrog by offering still more sweeping arms cuts and increased economic assistance to Moscow.
More, however, will be required. One possible compromise is a treaty covering future Nato's relations with Russia, to be signed before the July summit of the alliance in Madrid at which the first invitations will be extended to former Warsaw Pact members, probably the Czech Republic, Poland and Hungary. The US is said to have an open mind on a treaty.
However officials here are pouring cold water on the notion of a "Big Five" summit of Russia, Britain, France, Germany and the US which would tackle European security issues. Expansion, these officials argue, is a decision in which all Nato members must be involved.