DONETSK, Ukraine — Separatists in eastern Ukraine proclaimed the birth of two new “sovereign” republics Monday after claiming victory in controversial self-rule referendums, and one of the regions promptly asked to join Russia.

Leaders of the self-declared Donetsk People’s Republic also demanded that Ukrainian security forces leave the separatists’ territory.

The statements represented a hardening of positions that could drag Ukraine closer to all-out civil war and is likely to intensify tensions between Russia and the West.

“Based on the will of the people and on the restoration of a historic justice, we ask the Russian Federation to consider the absorption of the Donetsk People’s Republic into the Russian Federation,” Denis Pushilin, a separatist leader, said at a news conference.

Leaders of the parallel Luhansk People’s Republic told a crowd in the region’s capital that they proposed to join with Donetsk to form a new republic called “Novorossiya,” or New Russia, Ukrainian news media reported. According to a spokesman, the leaders were also considering whether to stage a second referendum to ask people outright if they wanted to join Russia.

Russia responded cautiously, repeating an earlier call for negotiations within Ukraine. “We reaffirm the need for the immediate establishment of a broad discussion in Ukraine concerning its future state structure, involving all political forces and the country’s regions,” the Russian Foreign Ministry said in a statement.

Ukraine’s government has denounced the referendums as a “criminal farce” arranged by a “gang of Russian terrorists,” but it says it is willing to talk with regional leaders about autonomy.

The sentiments expressed in the referendums underline the urgent need for the Kiev government to negotiate with the separatists, perhaps offering meaningful autonomy, before the situation slips further out of its control, experts said.

“There are a very large number of people who are resentful towards Kiev,” said Adam Swain, a professor from the University of Nottingham, England, and frequent visitor to the region, adding that the Ukrainian government ignored these sentiments at its peril. “If Kiev wants to have any semblance of control in the region, they have no option but to start negotiating. It is crazy for them to reject this out of hand.”

The twin referendums — deemed illegal by the United States and the European Union — asked voters whether they supported “self-determination” for the Donetsk and Luhansk people’s republics, respectively. But separatist leaders were deliberately vague about what that meant, saying that the question of whether to seek federal autonomy within Ukraine, independence or absorption into Russia would be left to a later date.

Separatists said 89 percent of the people who voted in Donetsk and 96 percent of those in Luhansk supported self-determination. The result could not be independently verified, and the way the referendums were administered — by the separatists themselves — lacked international credibility.

Yet the vote appeared to reflect genuine and widespread mistrust of the interim government in Kiev, which came to power in February after pro-Russian President Viktor Yanukovych fled in the face of popular protests.

Most people who opposed the referendums simply stayed away from polling stations. Many of those who voted “yes” said they wanted to remain with Ukraine but had turned out to express anger at Kiev.