Making his first tour of the restive eastern regions of his country after coming to power seven weeks ago, Ukraine’s prime minister arrived here Friday promising to push for more local autonomy and to listen to regional concerns.

After last month’s annexation of Crimea by Russia, pro-Moscow protests in Ukraine’s eastern cities, with thousands of Russian troops on alert just across the border, have posed a critical and continuing threat to the integrity of the country.

NATO, meanwhile, rebutted Moscow’s charges that the alliance was exaggerating the Russian military presence on the Ukrainian border. Rejecting Russian claims that satellite images previously released by NATO showed military exercises conducted in August 2013, the alliance published new photos Friday that it said prove that the Russian military buildup occurred early last month.

NATO “stands firm in its assessment that Russian forces in the vicinity of the border with Ukraine number in the range of 35,000 to 40,000 troops and are equipped with infantry fighting vehicles, tanks, combat aircraft, logistics and artillery,” the allied command said on its Web site. “These ­forces are destabilizing to the region, which is why the North Atlantic Council has repeatedly called upon Russia to de-escalate the situation by withdrawing troops from the border with Ukraine.”

The photos were taken by Digital­Globe, a Colorado-based commercial vendor of satellite imagery, and were not altered or edited by NATO, the alliance said.

At the same time, NATO released a lengthy fact sheet that it said “sets the record straight” on Russian attempts “to divert attention away from its aggression against Ukraine.”

In eastern Ukraine, pro-Russian separatists have occupied key government buildings in Donetsk and Luhansk all week. The new government in Kiev is unpopular here, perceived as being dominated by Ukrainian nationalists.

After he arrived Friday, Prime Minister Arseniy Yatsenyuk convened a public session with the leading members of the local power structure, at which they agreed that they want Ukraine to remain a unified country. They called on the separatists to leave the buildings they are occupying and surrender their weapons.

In an attempt to meet some of the demands here, Yatsenyuk endorsed local elections for regional governors and said regions should be free to hold referendums on certain issues. He spoke in both Ukrainian and Russian, and he promised that there would be no attempt to downgrade the status of the Russian language.

“We wish to readjust powers among parliament, the president and the cabinet of ministers,” he said. “It is our joint task to balance power between the center and the regions.”

In a reminder of the serious issues underlying the political crisis in Ukraine, seven people were killed in Donetsk on Friday — on the job, in an accident at a state-owned mine that has been the scene of other fatal incidents in recent years. Many of the coal mines of the Donbass region are poorly maintained, and bribery can induce safety inspectors to look the other way.

Anger at corruption and the dismal state of Ukraine’s economy is shared across the political spectrum, regardless of region, ethnicity or language spoken.

Yatsenyuk began his meeting with a moment of silence for the dead miners. Later Friday, he visited another eastern city, Dnepropetrovsk, where he said that Ukraine must have a new constitution in place before the May 25 presidential election. Otherwise, he said, the winner of that election would try to write the constitution to suit his or her own needs. He said the new constitution should provide for a decentralization of authority.

Among those who appeared with Yatsenyuk in Donetsk were the new local governor, the mayors of other eastern cities and the business tycoon Rinat Akhmetov. A former close associate of the ousted president, Viktor Yanu­kovych, Akhmetov has tried to play peacemaker here.

He said he is against the takeover of buildings and in favor of negotiations. When he met with the separatists occupying the regional administration building here Monday, he said, he told them, “For me, Donbass is Ukraine.”

But the occupations in Donetsk and in Luhansk continued, ignoring a deadline set Wednesday by Interior Minister Arsen Avakov. He had warned that if the protesters did not leave the buildings by Friday, the government would force them out. But with Yatsenyuk making his visit here, there was no sign of a move to use force.

The prime minister said he is against using law enforcement to settle the issue if at all possible. The government has offered the protesters amnesty if they leave voluntarily.

Polls suggest that they have little support among the public.

In Moscow, Russian Foreign Minister Sergei Lavrov said his country has no intention of absorbing eastern Ukraine. He said it would not be in Russia’s interest to do so.