Alexander Korzhakov, head of the presidential security service, one of the most powerful men in Mr Yeltsin's inner circle, said more time was needed to allow people to "think calmly", warning that there were "entire regions" in Russia where the "civilised expression of people's will" is impossible. The first round of the election is scheduled for 16 June.
Although he said his remarks were personal, they will be seen as reflecting a broader view in the Kremlin that the elections cannot go ahead because of the risk Mr Yeltsin may lose to the Communist front-runner, Gennady Zyuganov.
"It is inadmissible that Russians again fight Russians," General Korzhakov told the Russian agency, Interfax, "The society is splitting ... the division of souls is dangerous." He urged executives, parliamentary officials and leaders of political parties to take heed.
His remarks follow speculation that the elections may be called off. Just over a week ago, 13 prominent industrialists and bankers published a letter in Russian newspapers calling for the leading political rivals to reach a compromise before a conflict erupted. Mr Zyuganov yesterday told Pravda that Mr Yeltsin's entourage was ready to deny the population their right to vote, but that "people will not put up with this".
There is no doubt many in the Yeltsin administration fear defeat, as they would lose jobs and face prosecution for illegally cashing in on the privatisation process. But postponing the election without the agreement of the Communists would be a huge risk.
Much of the Russian military is already demoralised and disillusioned by the President's handling of the Chechen war. While the 25,000 presidential guards under Mr Khorzhakov's command may defend the Kremlin in the event of unrest, the loyalty of the military is not a foregone conclusion.
General Korzhakov's remarks may have been intended to bolster rumours that the Communists are privately willing to do a deal with the Kremlin in return for policy changes and key posts. On the face of it, the scenario seems unlikely.
The Communists stand a good chance of winning outright. They know hostility to Mr Yeltsin in the regions is huge, and that he lags in the polls. Yet they also know the President controls much of the media, which is showing bias in its coverage, and is pouring money into deprived areas to win votes. In recent weeks, he appears to have narrowed their lead.
In spite of General Korzhakov's wishes, the odds are that the vote will go ahead, as Mr Yeltsin has promised, with a first round in June and a final round in July. A more compelling issue is what will Mr Yeltsin do if the result goes against him. If he loses by a small margin, he would have little difficulty massaging the vote.
It is widely accepted that his administration cooked the vote in the 1993 referendum on the constitution. But a large deficit would be difficult to fix. What would then happen is anybody's guess.