Pro-Russian separatists defied international criticism by holding elections on November 2 in areas under their control in eastern Ukraine.
Residents in separatist-controlled areas voted for leaders and so-called "people's councils" for their "people's republics."
Russia's Interfax news agency, citing an exit poll, said that in the "Donetsk People's Republic," incumbent leader Aleksandr Zakharchenko was expected to win with 81 percent.
Results from neighboring Luhansk, however, were expected later because some polling stations remained open.
The leader of the "Luhansk People's Republic," Igor Plotnitsky, is widely expected to win.
The early results came as Ukrainian President Petro Poroshenko called on Russia to denounce the vote.
In an online statement, Poroshenko described the elections as a "farce, [conducted] under the barrels of tanks and machine guns."
He added: "I count on Russia not to recognize the so-called elections because they are a clear violation of the September 5 Minsk protocol, which was also signed by Russia's representative."
In a statement, European Union foreign policy chief Federica Mogherini called the vote an "obstacle to peace" and said the EU will not recognize the elections.
But the Russian Foreign Ministry said it "respects the will of the people of southeast" Ukraine.
"The elected representatives received a mandate to solve the practical tasks regarding the restoration of normal life in the regions," Interfax quoted the ministry as saying.
Ukraine’s Security Service said the vote violates Ukraine’s constitution and resembles an illegal “power grab.”
It also announced that it has opened a “criminal probe” against the organizers of the vote.
Earlier on November 2, Ukrainian military spokesman Andriy Lysenko said Russia had launched an “intensive deployment of military equipment and personnel” from Russian territory into parts of eastern Ukraine that are controlled by pro-Russian separatists.
Voters cast their ballots at a polling station in Donetsk.
AFP reporters near Donetsk said they saw a military column of about 20 trucks, some carrying antiaircraft guns, heading toward the government-held airport, although it was not clear whether they were new forces.
Several other Western media outlets also reported witnessing heavy movements of troops near Donetsk.
Among them, reporters for the news sites Buzzfeed and Mashable tweeted that they had seen a large military column.
Buzzfeed's Max Seddon wrote: "31 unmarked Kamazes (military trucks) just drove past towards Donetsk. Anti-aircraft weapons, ammunition boxes, radar systems, a bus of gunmen."
Two voters walk past pro-Russian rebels at a polling station in Donetsk.
In Donetsk, correspondents reported pro-Russian gunmen inside and outside several polling stations as voters were casting ballots.
The Ukrainian government, the United States, the European Union, other Western countries, and UN Secretary-General Ban Ki-moon have said the November 2 elections are illegitimate and will not be recognized.
The elections were not regulated by Ukrainian law or overseen by the Ukrainian Central Election Commission.
The vote was not observed by international monitors from bodies such as the Organization for Security and Cooperation in Europe (OSCE), but separatist officials claimed they had between 30 and 70 observers from several foreign countries and places like the breakaway Georgian republic of Abkhazia.
Russian Foreign Minister Sergei Lavrov said Moscow will "of course recognize the results" of the elections.