This week Moscow returned three Ukrainian naval ships that it captured in the Kerch Strait in November 2018 following a maritime skirmish between the two countries. That gesture came after France said it would host a long-delayed peace summit including the leaders of Ukraine, Russia, France and Germany on Dec. 9.

Last month, Moscow and Kyiv agreed to withdraw troops from the front line in eastern Ukraine and hold elections in the contested region.

Mr. Zelensky said on Tuesday that Ukraine wants to negotiate a deadline at the December summit for the return of the country’s territories from Russia, which annexed the country’s Crimean Peninsula in 2014.

Russian President Vladimir Putin has made clear that he regards Ukraine to be an integral part of Russian territory. The nations are “two parts of one and the same people,” he said in September.

Mr. Zelensky, 41 years old, faces resistance at home to his peace efforts. Many Ukrainians, including far-right nationalists who came out in the thousands in recent weeks to protest the plan, accuse the president of capitulating to Moscow.

Critics fear a vote in separatist-held eastern Ukraine could pave the way for pro-Russian separatists to gain power in the east, making it easier for Moscow to influence Kyiv’s domestic and foreign policy.

The Ukrainian president, a former comedian and political neophyte, rejects claims that he is surrendering to the Kremlin and insists that bringing peace to Ukraine is his ultimate goal.

As rallies were held across Ukraine last month, Mr. Zelensky addressed the concerns of war veterans. “I understand your fear,” he wrote on Facebook. “You rightly do not want what you fought for to be in vain. I promise you as the president of Ukraine and the commander in chief of the Armed Forces that I will never allow this.”

He told the service members in the Donetsk region last month that Ukraine is an independent, sovereign, unitary state, and its military would defend these principles embodied in the country’s Constitution.

Ukraine’s battle with Russia has made Kyiv more reliant on support from Europe and the U.S. and a target for the competing ambitions of Moscow and Washington.

Mr. Zelensky has found himself walking the same tightrope that Ukraine has been navigating for decades.

The opportunity for Moscow to overpower Kyiv is made more potent by Mr. Zelensky’s position at the heart of a U.S. House impeachment inquiry into whether President Trump held up U.S. aid to Ukraine for his own political gain.

“Right now, [he] is trying to balance different inter-political [foreign] interests and national interests of Ukraine,” said Alyona Getmanchuk, director of the New Europe Center, a think tank in Kyiv. “For Ukraine, the U.S. is the No. 1 security partner. It is crucial to keep bipartisan support in the U.S., especially now when there is a revival in peace negotiations with Russia.”

The U.S. and Europe have fiercely defended Kyiv, slapping sanctions on Russia for its aggression in Ukraine and providing vital economic and military aid to Ukraine, which has been drained by years of simmering violence.

Days after Mr. Zelensky was elected in April, Mr. Putin made it easier for residents of Ukraine’s separatist territories to get Russian passports. Supporters of the new Ukrainian president depicted the move as an attempt to intimidate him.

Mr. Zelensky, however, proceeded to try to open a line of communication with Mr. Putin. He repeatedly underscored his intentions to ease tensions with Russia and conducted a prisoner swap with Moscow. The exchange included two dozen Ukrainian sailors who were detained when the naval ships were seized.

Ukraine’s Defense Minister Andriy Zahorodniuk said on Monday that he didn’t see the return of the ships as an act of good will.

“I view these events as nothing else but the enforcement of last May’s International Tribunal for the Law of the Sea ruling by the aggressor state,” he wrote on his Telegram channel, according to the Interfax news agency. The ruling in May obliged Russia to immediately return the vessels.

Some critics said they don’t believe the Kremlin has good intentions, given the determination that Mr. Putin has shown in trying to exert influence over Ukraine and keep the former Soviet Republic, today the second-poorest country in Europe after Moldova, within Russia’s orbit.

For example, Russia is moving ahead in building Nord Stream 2, a pipeline that would carry natural gas from Russia to the West through the Baltic Sea—and deprive Kyiv of fees it collects on the Russia gas that currently transits through its territory.

Some observers even question whether Russia really wants to make peace, charging that it is in Russia’s interest to prolong the instability and conflict in eastern Ukraine’s Donbas region.

“While the war in Donbas is ongoing, Ukraine is unlikely to become a member of NATO or the European Union,” said Volodymyr Fesenko, director of the Kyiv-based Penta Center for Political Studies, an independent think tank. “It’s unlikely that Ukraine will become a success story. And a weak, unsuccessful Ukraine is a benefit to Russia.”

While the war continues, the annexation of Crimea is pushed out of the spotlight, allowing reinforcement of the widely held belief that the region will never be returned to Ukraine.

“For centuries, Ukrainians have been fighting against the imperial ambitions of Russia,” said Yuriy Gudymenko, co-founder of Democratic Axe, which describes itself as a right-liberal political organization. “We understand that Russian imperialistic ideas cannot exist without having Ukraine be part of its empire. We are afraid of Ukraine being a part of Russia, a satellite of Russia.”

For Moscow, Ukraine’s importance is rooted in cultural, linguistic and religious ties that predate the 18th century creation of the Russian empire. Conquered by Soviet Russia in 1920 and once the breadbasket of the U.S.S.R., Ukraine is viewed by Mr. Putin as an intrinsic part of Russia’s heritage and the Slavic brotherhood.

“Russians and Ukrainians are one people…one nation, in fact,” Mr. Putin said in a June interview with U.S. filmmaker Oliver Stone, according to a transcript published by the Kremlin. “When these lands that are now the core of Ukraine joined Russia…nobody thought of themselves as anything but Russians.”

Russia has long loomed over Ukrainian domestic politics. In 2004, a rigged presidential election handed victory to pro-Russian candidate Viktor Yanukovych over opposition leader Viktor Yushchenko —whose possible victory stood to challenge Moscow’s autocratic model of governance.

After election fraud sparked mass protests, Ukraine’s Supreme Court annulled the results and Mr. Yushchenko went on to win. The Kremlin denied any interference in the vote.

Mr. Yanukovych, who made a comeback in 2010 to assume the presidency, fled to Russia after violent civil unrest erupted in 2014 following his abrupt abandonment of a planned partnership accord with the European Union. Pro-Western businessman Petro Poroshenko was subsequently elected president.

Kyiv’s troubled relations with Moscow compounded Mr. Poroshenko’s failure to fulfill promises to end pervasive corruption and improve living standards. Mr. Zelensky beat the former president handily in an April vote.

Now his compatriots want him to avoid being conquered by Mr. Putin.