In an effort to draw voters to an election lacking suspense — as the existing rebel leaders, including Mr. Zakharchenko, a former electrician, seem sure to stay on — polling stations opened Sunday in Donetsk schools with gigantic piles of cabbage, potatoes, carrots, beets and onions in the yards outside; at one site, the vegetables were sold at far below market price. At other sites organizers gave the vegetables away. Several polling stations offered live entertainment, ranging from a three-member Slavic folk band to a man playing an accordion.

In a practice common in authoritarian post-Soviet countries, one candidate in Donetsk endorsed his opponent, Mr. Zakharchenko, in the race. In a 2012 presidential race in Turkmenistan, for example, nominally competing candidates gave speeches standing in front of giant posters of the incumbent, who won.

“We don’t have any differences, none at all,” Yuri V. Sivokonenko, the head of a police union and candidate for head of state, said in an interview. “I didn’t ask people to vote for me, because I don’t have any differences in principle with Zakharchenko.”

Mr. Sivokonenko said he had put up no campaign advertising because he lacked funds for it. A deputy speaker of the Parliament of Novorossia, Aleksandr Kofman, was also on the ballot but ran a low-profile campaign. No candidates ran in open opposition to the current rebel leadership. The overriding goal of the election, Mr. Sivokonenko said, was to boost the legitimacy of the separatists’ state. “By the end of the day, the Donetsk People’s Republic will have a new status,” he said. “The election confirms our status as a state.”

Posters and billboards put up by the rebel central election commission echoed this sentiment. “When Ukraine died in our hearts, the Donetsk People’s Republic was born,” one poster at a polling station said. It presented the advantages of the elections as allowing the rebel state to “retain taxes and pay pensions,” guaranteeing the right to speak Russian and opening the Russian market for Donetsk-area exports.

The speaker of the Donetsk Supreme Soviet, Boris O. Litvinov, said in an interview there were only “very, very small differences” between the candidates running, but the election was necessary. “Nobody will speak with revolutionaries these days,” he said. “That’s just the way of the world. We need a democratic state.”

Several voters said the election would compel Kiev to negotiate with separatists and end the war. “Now we will have a leader who can cooperate with other leaders,” Tatyana Buncherenko, 41, a railroad employee, said. “I will vote for Zakharchenko,” she said.