Many Russian soldiers are dying in the fighting in Ukraine, according to the deputy secretary general of the North Atlantic Treaty Organization. This blunt declaration makes it increasingly difficult for Russian President Vladimir Putin’s government to maintain the claim that the Kremlin has no involvement in the ongoing conflict on its border.

“Russian leaders are less and less able to conceal the fact that Russian soldiers are fighting – and dying – in large numbers in eastern Ukraine,” Alexander Vershbow said at a conference in Latvia on Thursday, adding that NATO believes the deaths are making the conflict increasingly unpopular among Russians.

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The fighting in the eastern part of Ukraine, which began last year after Russian troops invaded the country’s Crimean peninsula, has dropped off dramatically since a ceasefire agreement as reached last month. Yet skirmishing continues, particularly in the area between rebel-controlled territory and the city of Mariupol, widely seen as the next target of the Russia-backed rebels.

In recent days, evidence has been accumulating that the Russian people are starting to question their government’s claim that any Russian soldier fighting in Ukraine is doing so as a volunteer – and while on vacation from standard duty.

In a powerful story published on Tuesday, Vice media reporter Lucy Kafanov interviewed the parents of Russian soldiers whose dead bodies, with wounds that could only have been sustained in combat, were returned to their hometowns. Certificates accompanying the soldiers’ bodies claimed the men had been killed at a “point of temporary dislocation.”

Russian newspaper Novaya Gazeta, one of the few independent Russian news outlets still in operation, published an interview earlier this week with a Russian soldier – a tanker – who suffered grisly wounds after his unit was deployed to fight in Ukraine, he said.

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On Thursday, U.S. Deputy Secretary of State Anthony Blinken said that continued efforts by Russia to prevent Ukraine from maintaining control over its sovereign territory – particularly its border with Russia – would result in an increase in the financial sanctions that Western countries have imposed on Moscow over the past year.

The restoration of Kiev’s control over the border is critical, Blinken said. “Unless that happens and until that happens, Russia will always have, and President Putin will always have, the possibility to turn up the dial any time he wants,” said Blinken, “sending weapons in, sending men in, materiel in, and reigniting the conflict.”

Blinken said that failure to allow Ukraine to control its own borders would prevent any lifting of economic sanctions imposed on Russia by the U.S. “The choice is clear, and it’s up to President Putin,” Blinken said.

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The Kremlin, for its part, remains defiant. The U.S. recently announced it would be sending a few hundred troops to Western Ukraine, far from the fighting, to help train Ukrainian soldiers.

Kremlin officials on Thursday condemned the move as a “provocation” that could further inflame the situation in Ukraine. Alexander Lukashevich, a spokesperson for the Russian Foreign Ministry, said Thursday that the U.S. trainers threaten Russia’s security.

“Kiev authorities and all the Ukrainian people should think about the possible consequences of such steps,” he said. “It is evident that they are not trying to bring peace to the country,” Lukashevich concluded.

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