Russian officials had announced earlier that a single warship would depart for the region on Friday.
Yeltsin also called for a meeting of the foreign ministers of the G-7 leading industrialized nations and Russia on halting the NATO attacks. But because six of the seven G-7 nations were participating in the NATO operation, it appeared unlikely they would agree to such a meeting.
Russia has stressed it will not become involved in the conflict militarily, but it has angrily denounced the air strikes.
One Russian warship was to depart Friday for the Mediterranean and more could follow shortly if Yeltsin approves them, officials said.
Turkey, which controls the Bosporus Straits through which Russian ships must pass from the Black Sea to the Mediterranean, said it had agreed to allow eight warships to pass. Four ships could move through the straits this weekend, three more next Tuesday ,and one next Thursday.
Secretary of State Madeleine Albright spoke with Russian Foreign Minister Igor Ivanov by telephone late Wednesday to express concern about the naval deployment, Russian news agencies reported. Ivanov said the move was to ensure Russia's security and give Moscow a clear idea of what was happening in the region, reports said.
The Russian Foreign Ministry Thursday criticized the U.S. fears, calling them "absurd in light of NATO's huge forces in the Balkans," the Interfax news agency reported.
Even though Russia has decided to deploy ships, Moscow "has no intention of interfering in the current conflict around Yugoslavia," the report said.
CBS News Military Consultant Ret. Col. Mitch Mitchell says that the ships should pose no threat to U.S. forces. "They're there to make a statement and see what is going on in the Mediterranean," he explains.
He adds, "I don't think that is any threat to us at all, though it might give the Serbs some reason to hope, and false reason, at that. The Russians are not going to take us on, for sure. They're not going to use those naval forces against us. It is just a training mission."
In an address Thursday on Russian television, Yeltsin said, "Despite Russia's resolute actions, NATO military action against Yugoslavia continues to escalate. Such an escalation threatens to lead to a grave disaster, and not only for Europeans. That must not be allowed."
At the same time, officials said, Russia would increase its military preparedness, but no further details were given.
NATO attacks against Yugoslavia have "raised new objectives for the Russian armed forces," Ivanov said after senior officials discussed the situation at the Kremlin.
Ivanov said Thursday that Russia was still looking for ways to restar peace talks on the Kosovo crisis and several initiatives were under review, but he gave no details. A Russian peace mission headed by Prime Minister Yevgeny Primakov failed to produce a breakthrough Tuesday in Belgrade.
The Kosovo crisis has put the Russian government in a difficult situation, domestically and overseas. It opposes the NATO air strikes, but has few ways to counter them, while its domestic opponents are using the crisis to accuse the Yeltsin administration of weakness.
The Russian military is in shambles and the nation badly needs Western loans to crawl out of one of the worst recessions ever experienced by an industrial country.