The previously unannounced trip to Sochi stoked a frenzy of rumour about the physical and political health of Mr Yeltsin, 63, who retired to the coast last Monday for an unscheduled fortnight's break.
The main evening news last night on Russian television featured Mr Yeltsin chatting with Mr Chernomyrdin at a picnic table in the garden.
The Kremlin shrugged off talk of a crisis, describing the Black Sea rendezvous as routine. At the same time, the general prosecutor's office was said to be investigating an article in a newspaper, Obshchaya Gazeta, which purported to give details of a planned coup against Mr Yeltsin.
Civil war and coups are the small change of Russian political discourse. It was none the less odd that Mr Chernomyrdin chose to fly to Sochi instead of keeping an appointment in Moscow with the visiting managing director of the IMF, Michel Camdessus.
Mr Camdessus is in Russia to decide if the IMF should grant a dollars 1.5bn (pounds 1bn) loan, the second tranche of a special fund badly needed by Moscow to unblock other stalled credits. Talks have not gone well. The IMF challenges Moscow's ability to stick to a tight budget presented to parliament last week by Mr Chernomyrdin. Officials quoted by Tass complain of Mr Camdessus' 'unconstructive position'.
A presidential spokesman, Anatoly Krasikov, insisted the Prime Minister's decision to see Mr Yeltsin involved 'nothing ultra-urgent'.
Itar-Tass, the national news agency, suggested that Mr Yeltsin had summoned Mr Chernomyrdin because of a rapidly deteriorating political situation in Moscow, where foes last week formed a new anti-reform coalition called Accord for Russia.
'The two leaders are due to discuss pressing political economic problems which have accumulated since the President left,' said Tass. It gave a long list of problems, ranging from IMF negotiations to newspaper reports suggesting Mr Yeltsin's health could prompt a palace coup. 'All this will make the working meeting in Sochi both important and difficult,' the news agency added.
Mr Yeltsin, though vastly stronger on paper thanks to a new constitution adopted last December, has rarely looked more vulnerable. His call for a political truce, a newly drafted manifesto called a 'memorandum of civil peace and concord in society', has met only ridicule. His enemies from last October, when Moscow teetered on the brink of civil war, are all out of jail thanks to a a parliamentary amnesty and back on the offensive.
Mr Yeltsin has been dogged by persistent reports of serious ill-health. He has been suffering from what aides describe as a cold since late January.
Speculation about Mr Yeltsin's health has focused attention on an important change in Russia's constitution. The new text makes the prime minister the president's stand-in in event of serious illness. But the Kremlin yesteday dismissed talk of serious illness as 'deliberate disinformation' aimed at 'aggravating the situation and destabilising society'.Reuse content