Ukrainian leaders said Wednesday that their country was starting to stabilize, as the Kremlin repeated its assurances that it was pulling its military back from the border and pro-Russian separatists in the east continued to be on the defensive.

Ahead of Sunday’s presidential election, fears that Ukraine was on the verge of a bloody civil war — or being invaded by Russia — appeared to recede. Russian officials made conciliatory gestures, while Ukraine’s wealthiest man escalated his campaign against separatists in the country’s industrial heartland in the east, the Donetsk Basin, also known as Donbas.

“Those who represent and control Donbas have declared that no bandit republic will run Donbas or Ukraine,” Arseniy Yatsenyuk, the acting prime minister, said during a third round of national unity talks in the shipyard city of Mykolaiv. “I consider this a result of our joint work.”

The relief came as billionaire Ukrainian businessman Rinat Akhmetov renewed an impassioned plea to push back against the separatists, who have taken over buildings and cities in the east.

“Fight, fight and fight again for your happiness, your present and your future!” the tycoon said.

Some critics having questioned Akhmetov’s timing, saying that he appeared to have waited until he knew that Russia was unlikely to invade before deciding last week to form worker patrols to help police restore order in Mariupol, an industrial port city in the southeast. Nonetheless, many Ukrainians welcomed his efforts.

Russia has decided to pull its troops back from its border with Ukraine “as an additional step to help create a favorable environment for the upcoming presidential election,” President Vladimir Putin told reporters in Shanghai on Wednesday. The Russian leader called the election a “positive step” but also said that “it will be very difficult for us to build relations with those who come to power with punitive operations still underway in southeast Ukraine.”

The Pentagon said Wednesday that it had seen troop movements along the Ukrainian border but that it was not clear whether they were part of a pullout.

“It’s impossible at this early stage to tell whether or not this movement that we’re seeing is simply more of the same or if this is preparations for a broader withdrawal,” a Pentagon spokesman said.

If a pullout occurs, Secretary of State John F. Kerry said during a trip to Mexico City on Wednesday, “and we’re watching carefully, that’s extremely constructive.”

Russia’s Defense Ministry said Wednesday that Russian troops in regions along the Ukrainian border have, “in the past 24 hours,” packed up their gear and “are now heading to train stations and airfields for embarkation,” according to the news agency Interfax.

But the commander of Russia’s air force said Wednesday that a scheduled “international competition” — in which Russian warplanes will “compete” in firing missiles and bullets at ground targets — would proceed in the vicinity of the Ukrainian border throughout the coming week, despite Kiev’s objections, the state-run Ria Novosti news agency said.

The exercises will get underway Sunday, when Ukrainians head to the polls.

Kunkle reported from Donetsk. Daniela Deane in London and Abigail Hauslohner in Moscow contributed to this report.