Although Mr Chernomyrdin said his boss was getting better and said his advice would be sought before important decisions were taken, the news of the partial transfer of responsibility was certain to provoke fresh speculation about the Kremlin leader's health and his chances of remaining in power.
A brief appearance by Mr Yeltsin, 64, on television, his first since he went in to hospital last week, did little to inspire confidence. Shown sitting almost motionless in a chair opposite Mr Chernomyrdin, the President slurred as he said: "Subjectively I feel not bad. The recovery's going according to plan. There are no fears now."
Mr Chernomyrdin, who was allowed a 30-minute meeting with Mr Yeltsin in Moscow's Central Clinic, suggested that the President's relapse might have happened because he went back to work too quickly after his first heart attack in July.
"I think the President just needs to complete his course of treatment and everything will be all right," he said.
He even went on to suggest Mr Yeltsin might still run in presidential elections due next June.
"The Russian President will soon be fit and his participation in the next presidential elections is a matter of technicalities," he said.
But for the time being, Mr Yeltsin must rest. And so Mr Chernomyrdin will co-ordinate the work of the foreign, defence, security and interior ministers.
"The President has to be partially relieved of these duties to give him a better chance to recover," he said.
"But of course we seek the President's advice on all key questions."
The four "power ministers" are heavily burdened, with the Foreign Minister striving to raise Russia's profile in international affairs, especially the search for peace in Bosnia, and the other ministers bogged down in the Chechnya crisis.
Reporters asked if Mr Yeltsin had himself thought of being relieved of the responsibility of making sure they work smoothly together.
"I could see in his eyes that Chernomyrdin should work harder," the Prime Minister replied.
Most of Mr Yeltsin's Communist and nationalist opponents are maintaining a tactful silence, aware that they could damage their chances in December's parliamentary elections by being seen to kick a man when he is down.
But yesterday Yuri Skokov, who is in alliance with the nationalist retired army general Alexander Lebed, voiced what they were all thinking. Mr Yeltsin had "failed as a president" and "exhausted his abilities in the post" but his "ego" prevented him from admitting this, Mr Skokov said.
However, support for Mr Yeltsin came from the head of the Forward Russia movement, the market reformer Boris Fyodorov.
It was too early to write Mr Yeltsin off, he said, condemning government officials for "leaving the ship even before it has started to sink".
In the absence of detailed medical bulletins, it is difficult to assess Mr Yeltsin's true condition and future prospects. All that can be said for certain is that his illness has greatly complicated the political picture in the run-up to the elections.
The race for parliament, seen as a test-run before the presidential election, was almost certainly one of the main topics of discussion between Mr Yeltsin and Mr Chernomyrdin. The Kremlin leader made clear earlier in the week that he was concerned about election officials barring a number of parties from taking part on technical grounds.
Yesterday the Supreme Court ruled that the Derzhava (great power) movement of the former vice-president Alexander Rutskoi should be reinstated.
A similar verdict was widely expected in the case of the liberal Yabloko bloc.Reuse content