Meanwhile, the economy continued in turmoil and the Russian people were flocking to stores to clear goods off shelves before prices rose yet again. Fears of violence were voiced by some politicians.
The president has said that Viktor Chernomyrdin is his only choice to lead a new government that must deal with the country's worst economic crisis since the 1991 breakup of the Soviet Union.
But parliament's lower house, the State Duma, overwhelmingly turned Chernomyrdin down Monday for a second time.
Yeltsin had not named anyone by midday, which fueled speculation that he might be considering an alternate candidate.
The Communists and their allies say they have nine alternate candidates, including Moscow Mayor Yuri Luzhkov. The liberal Yabloko party on Monday has suggested Foreign Minister Yevgeny Primakov.
However, ultranationalist Vladimir Zhirinovsky said Yeltsin planned to stick with Chernomyrdin, who was prime minister for five years before the president fired him in March.
"It will be Chernomyrdin and no one else," Zhirinovsky said.
Communist leader Gennady Zyuganov said his party, the largest in the Duma, would never accept Chernomyrdin and said renominating him would lead to the "complete paralysis of the entire political process."
If the Duma rejects Yeltsin's candidate again, the constitution calls on him to dismiss parliament and call new elections within three months. Yeltsin would rule by decree, along with an interim government, until the new legislature is seated.
During all the political chaos, Russia's economy has continued a downward spiral.
The government will hold talks Thursday on an emergency federal budget for the remainder of the year, and plans for the 1999 budget will have to be revised, government spokesman Igor Shabdurasulov said.
Moscow's interbank currency exchange failed to provide a formal ruble rate against the dollar for the second straight day Tuesday, leaving the market without an agreed-upon level for the Russian currency.
Prices have been increasing daily and shoppers are clearing out store shelves in anticipation of even higher inflation. Long lines at gas stations began forming Monday as motorists filled up before prices rise.
In some Moscow markets Monday, the caviar was less expensive than suddenly hard-to-find imported toilet paper, reports CBS News Moscow Correspondent Richard Threlkeld.
Food prices are now so high that the present minimum wage of about $4 a month will now buy just a quart of cooking oil, two cans of meat preserves, and a single loaf of bread - if it can be found.
"I have no money to feed my two grandchildren," says a pensioner named Maria. "This is all the politiians' fault...they should be chucked out."
When already fed-up Russians turned on their televisions Monday, they could see their politicians still squabbling. Russia has officially been without a government for three weeks now, and the country appears no closer to getting one.
That's why some Russian politicians and newspapers are now warning that violence, a grim scourge that has repeatedly checked Russia's progress in the 20th century, could return as economic turmoil has again impoverished the Russian people.
The head of the main opposition Communist Party, Gennady Zyuganov, said on Monday the tensions and frustrations in Russia parallel those in 1917 before the Bolshevik revolution.
Chernomyrdin said opposition deputies were pushing the country down the path of Indonesia, which has been hit by violence and riots this year.
But Alexei Lukyanov, 29, who imports clothing from abroad, was in Indonesia before unrest broke out this year, and said the troubles in Russia are different.
"There was a different situation there because 90 percent of the business leaders are Chinese and Indians, not Indonesians, and the people were against them," he said as he waited for his daughter outside a Moscow school.
"I think civil war is unlikely, because Russian people are very patient, and it's hard to push them in that direction," he said. "There won't be war."