Earlier this week, Russian President Vladimir Putin announced he was pulling his country's troops back from its border with Ukraine. Thursday, NATO officials said they're seeing signs Russia's troops might withdraw, although many soldiers remain near the border.

NATO's leader reports seeing "limited Russian troop activity" close to the border, which could suggest "some of these forces are preparing to withdraw."

Tensions in the area are high as Ukraine prepares to hold national elections Sunday. Putin said Wednesday that the pullback was meant to create "favorable conditions for Ukraine's presidential vote and end speculation," The Associated Press reported.

As Ukraine prepares for the vote, its forces have struggled to secure areas in the country's east. Separatists in the Donetsk region attacked a checkpoint Thursday, and at least 11 soldiers reportedly were killed.

Putin said Monday that he ordered Russia's troops to return to their home bases. As we noted at the time, it marked the second time the Russian leader has issued this kind of order.

Here's an update from NATO Secretary General Anders Fogh Rasmussen, issued Thursday:

"Late yesterday, we have seen limited Russian troop activity in the vicinity of the border with Ukraine that may suggest that some of these forces are preparing to withdraw. It is too early to say what this means, but I hope this is the start of a full and genuine withdrawal.

"At present, most of the previously deployed Russian force remains near the Ukrainian border and we see continued Russian exercises in the same area.

"If we see any meaningful, comprehensive and verifiable withdrawal, I would be the first to welcome it. This would be a first step from Russia into the right direction of living up to its international commitments, especially as Ukraine is preparing to hold important presidential elections on Sunday."

Rasmussen added that "I hope we will see a political and diplomatic solution to the crisis in Ukraine."

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NATO Says It Sees 'Limited' Russian Troop Activity Near Ukraine