Russia has launched what it calls referendums on joining its country in four Ukrainian regions it occupies.
Kyiv calls the move an illegal sham carried out by Russian-backed separatists.
The separatists are operating the voting in Donetsk, Luhansk, Zaporizhzhia and Kherson.
Leonid Pasechnik, a pro-Russian separatist leader, said, "Today is the first day of the referendum, and we are voting to join the Russian Federation."
A US think tank says Russian-backed authorities in Luhansk are forming armed groups. They are going door-to-door forcing residents to cast their ballots.
One woman told NHK she might have no choice about voting.
She said, "I don't want to go to vote, but if they come to my house, I have no choice."
Ukrainian President Volodymyr Zelenskyy has condemned the referendums. He said Russian leaders used the same tactics in Crimea and Donbas in 2014.
Zelenskyy said, "The farce of preparing sham referendums in the occupied territory echoes what happened in 2014 in Crimea and Donbas. Russia itself is burying the chances of negotiations with its own hands."
In Russia, protests spread across the country after President Vladimir Putin announced a partial mobilization on Wednesday.
A Russian human rights group said over 1,300 demonstrators had been detained as of Thursday.