By Oren Liebermann and Barbara Starr, CNN

(CNN) -- Top US national security officials have spoken with their Ukrainian counterparts, and America's top general held a call Wednesday with his Russian opposite number amid concern over Russian military activity in Crimea and eastern Ukraine, including what the US deemed a violation of a ceasefire by Moscow that led to the deaths of four Ukrainian soldiers last week.

"Russia's destabilizing actions undermine the de-escalation intentions that had been achieved through [last year's agreement]," chief Pentagon spokesman John Kirby said Wednesday. "Additionally, we are aware of Ukrainian military reports concerning Russian troop movements on Ukraine's borders."

Secretary of State Tony Blinken reaffirmed the "unwavering support" of the United States for Ukraine's territorial integrity in the face of "Russia's ongoing aggression in the Donbas and Crimea," according to a readout of his call with Ukrainian Foreign Minister Dmytro Kuleba Wednesday. Chairman of the Joint Chiefs of Staff Gen. Mark Milley also spoke to the top Ukrainian general Wednesday, while national security adviser Jake Sullivan spoke with his Ukrainian counterpart at the beginning of the week.

The Pentagon had grown increasingly concerned after military intelligence reports assessed that some 4,000 heavily armed Russian forces had been observed moving in Crimea, according to a US defense official. "It was not totally clear what they were up to," the official said, adding that the US now believes on further assessment it may have been part of a Russian military exercise. Part of that assessment was based on calls with Ukrainian officials who also viewed the Russian activity as an exercise.

If so, the movement of so many Russian military personnel was a large exercise and may be a deliberate message from the Kremlin to the Biden administration about Russia's strength in the region and its ability to challenge US allies, the official said.

This comes as NATO countries on Monday scrambled jets 10 times to track an unusually high level of Russian military flights over a large area of Europe including the North Sea, the Black Sea and the Baltic Sea. NATO jets wound up conducting six intercepts in a six-hour period.

The Biden administration is taking a tougher approach to Russia, and Ukraine is only the latest source of tension between the two adversaries. The White House unveiled a raft of sanctions against Russian officials and entities at the beginning of the month over the poisoning of opposition leader Alexey Navalny. President Joe Biden then warned that Russian President Vladimir Putin would "pay a price" for his efforts to undermine the 2020 US elections and went on to call Putin a "killer." Meanwhile, the administration is expected to impose more sanctions on Russia over election interference and the SolarWinds cyberattack.

On Wednesday, Milley spoke with his Russian counterpart, Gen. Valery Gerasimov. While the topics the two generals discussed have not been made public, behind the scenes the Defense Department has been concerned for the last several days about the build-up of Russian troops and equipment along the Ukraine border. The Defense Department recently raised the so-called "watch condition level" on that region to gather updated intelligence assessments on Russian activity and intentions, while monitoring any potential threats. The New York Times was first to report that development.

Russia blamed Ukraine for renewed fighting in eastern Ukraine. Kremlin spokesman Dmitry Peskov said this week that Russia was concerned about "Ukraine's provocations," but he said he hoped it would not escalate to fighting.

But Ukraine warned of a series of Russian violations of the ceasefire, including two incidents of mortar fire and large-caliber machine gun fire that led to the death of the four Ukrainian soldiers last Friday. On Tuesday, Ukraine accused Russia of violating the ceasefire seven times, prompting the country's parliament to call for an increase in political and economic pressure on Moscow.