Russia said Tuesday that it was reviewing its military strategy in the face of expected NATO plans to establish a rapid-reaction force capable of deploying quickly to Eastern Europe, ratcheting up tensions ahead of a NATO summit this week.

The review of the Kremlin’s military doctrine came as Russian-backed rebels made fresh gains Tuesday on the ground in eastern Ukraine, where they have swiftly recaptured territory after appearing close to defeat just weeks ago. Kiev and its allies have said Russia has sent in its own troops to tip the balance in favor of the rebels, a charge the Kremlin denies.

NATO leaders meeting later this week in Wales are expected to endorse the creation of a military force of about 4,000 troops capable of deploying to Eastern Europe on about eight hours’ notice.

Russia’s intent to improve its plans to counter NATO forces, announced without further detail Tuesday by a top Kremlin official, brings the sides closer to a large-scale armed confrontation than they have been at any other time since the end of the Cold War.

“The issue of NATO military infrastructure encroaching on our borders, including through the expansion of the alliance, will remain among the biggest military threats to the Russian Federation,” Mikhail Popov, deputy head of Russia’s Security Council, told the state-run RIA Novosti news agency.

Western officials in recent years told the Kremlin that NATO was not focused on Russia, Popov said. But now, he said, the Kremlin’s long-term concerns about the alliance have been proved correct.

Popov’s comments came as Kremlin aides appeared to acknowledge reports that Russian President Vladimir Putin told a top E.U. official that “if I wanted to, I could take Kiev in two weeks.”

A top Kremlin aide, Yuri Ushakov, accused the E.U. official, Jose Manuel Barroso, of engaging in undiplomatic behavior by leaking the conversation, and he told the Interfax news agency that the quote had been taken out of context. He stopped short of saying that Putin had not made the remark. The Italian newspaper La Repubblica reported Monday that Putin had made the comment after denying that Russian troops were on Ukrainian soil.

Russian Foreign Minister Sergei Lavrov told a news conference in Moscow on Tuesday that Ukraine’s moves to join NATO were undermining efforts to end the war there. He called on the White House to use its influence on Ukrainian President Petro Poroshenko during his planned visit to Washington this month.

“The most important thing is the need to talk sense into the party of war in Kiev, and in large part only the United States can do this,” he said.

In Kiev, a Ukrainian military spokesman said Russian troops have been spotted in the rebel-held cities of Donetsk and Luhansk, as well as other places in eastern Ukraine. According to the spokesman, Col. Andriy Lysenko, they have also started hiding in forests around the region to avoid confrontations with local populations. NATO has estimated that at least 1,000 Russian troops have joined the fighting in Ukraine.

Lysenko said that 15 Ukrainian soldiers had been killed in the past day’s fighting and that Russian troops had shelled Ukrainian forces from both Russian and Ukrainian territory.

The continued assertions of direct Russian military intervention came as Ukraine’s defense minister warned of a “great war” with Russia, “the likes of which Europe has not seen since the Second World War.”

Rebel forces have turned the tide of battle and have captured large stretches of new territory in the past week, including near Mariupol, where separatist efforts were quashed in May. Rebels said Tuesday that they had captured several more roads that lead to the strategic port city.

Talks on Monday in Minsk, Belarus, to resolve the conflict ended without results, but all sides said Tuesday that they would continue the discussions later this week. The rebels’ representative at the talks, Andrei Purgin, said Tuesday in Moscow that anything short of independence from Ukraine would be unacceptable, a stance that Kiev is unlikely to agree with.

When pro-government forces were making quick strides last month against the rebels, it appeared unlikely that the Ukrainian government would settle for anything other than a full military victory in the east. The influx of aid from Russia may have been intended to sway the calculus and force concessions from Kiev.

Daniela Deane contributed to this report from Rome.