"There won't be any elections under the barrel of a gun," Zelenskiy said in response to criticism that his administration bowed to Russia's demands. "There won't be any elections there if the troops are still there."
Separatist leaders and the Ukrainian government also pledged to pull back troops from two locations in the Donetsk and the Luhansk regions early next week.
Zelenskiy insisted the local election would be held according to Ukrainian law, meaning all candidates and political parties should be allowed to run. Separatist leaders have rejected that idea in the past, saying they wouldn't allow Ukrainian parties that included nationalist politicians to run.
Both the separatists and Ukraine agreed the election will be considered valid as long as monitors from the Organization for Security and Cooperation in Europe determine they are free and fair, Zelenskiy said.
The Kremlin has denied providing military or financial support to the separatists despite overwhelming evidence. Russian troops were spotted in eastern Ukraine during crucial offensives, and the rebels themselves don't make it a secret they received weapons and training from the Russian military.
Moscow has tried to play down its involvement in eastern Ukraine in recent years, pulling back its troops and mostly relying on proxy forces. The separatists, in the meantime, re-branded their fighters as police or other law enforcement officers.
The election agreement was seen as the final hurdle before a summit between Zelenskiy, Russian President Vladimir Putin and the leaders of France and Germany, who have helped mediate the peace talks. French President Emmanuel Macro said earlier Tuesday that he expects the summit in the coming weeks.
Russia previously declined to sit down with Ukraine unless it signed an agreement on holding a local election.
Former Ukrainian officials and lawmakers who were voted out of office earlier this year following a landslide victory by Zelenskiy and his allies expressed concern Tuesday that Kyiv was giving up its sovereignty over the east by signing the accords.
Former parliamentary speaker Andriy Parubiy, in a Facebook post on Tuesday, slammed the plan for a local election as "an attempt to dismantle the Ukrainian state" and pledged to fight against what he described as "capitulation."
Parubiy's supporters and other nationalist activists gathered outside the Ukrainian presidential administration late Tuesday to protest the agreement, later moving to the Maidan. Some held a banner saying "No to capitulation!" Police stood watch.
In Moscow, officials and pro-Kremlin politicians welcomed the accords.
Alexei Pushkov, chairman of the information committee in the upper chamber of the Russian parliament, hailed the agreement as "our major achievement" and expressed hope that the four-way summit, the first one to be held since 2016, "could lead to a noticeable progress in (our) relations with Europe."
Moscow's recent outreach to Kyiv was seen as Russia's attempt to get the European nations to roll back at least some of the sanctions that were imposed on Russia in the aftermath of the 2014 annexation of Crimea and the start of the conflict in eastern Ukraine.
Associated Press writer Yuras Karmanau reported this story in Kyiv and AP writer Nataliya Vasilyeva reported from Moscow.