DONETSK, Ukraine — With a critical presidential election looming on Sunday, rifts are appearing among the patchwork of separatist groups that have seized control of public buildings in numerous cities in southeastern Ukraine.

In an interview on Wednesday, a rebel politician in Slovyansk said he did not recognize the authority of the self-proclaimed government of the Donetsk region and suggested he could use force to seize control.

Vyacheslav Ponomaryov, the self-declared mayor of the city of Slovyansk, where Ukrainian troops and anti-Kiev militias have engaged in sporadic fighting for several weeks, said that there was no contact between him and the new republic’s government and suggested he could order the city’s paramilitary groups to “restore order” in Donetsk.

“We are here fighting, and they are sitting around stuffing themselves,” Mr. Ponomaryov said by telephone from the city, which has been surrounded by Ukrainian military checkpoints and is in a region where shelling and shootouts have occurred in recent weeks. “It’s not a difference of opinion,” he said. “We have fundamentally opposing views.”