But the United States still believes that Russia doesn't plan to order its forces into its tumultuous neighbor, the official said on the condition of anonymity.
U.S. officials -- who are monitoring the area 24 hours a day -- have not yet seen signs that Russia is preparing to secure supply and transportation routes that would be crucial to any such movement, the official said.
Russian military activity levels observed by the United States also "appear to be within normal range," the official said.
Russian Foreign Minister Sergey Lavrov offered reassurances Thursday to U.S. Secretary of State John Kerry that the exercises were previously planned and were not being carried out because of the upheaval in Ukraine, echoing an earlier conversation between U.S. President Barack Obama and Russian President Vladimir Putin.
The Russian Defense Ministry has said the combat readiness evaluation is being carried out in territory overseen by the western and central military commands.
That puts some of the exercises near the Ukraine border.
"All in all, about 150 thousand military personnel of different services of the armed forces and military commands are involved in the check," Russian Defense Minister Sergey Shoigu said in a statement released by the ministry.
"Up to 90 planes, more than 120 helicopters, up to 880 tanks, over 1,200 defense equipment units and about 80 ships will be used."
U.S. Defense Secretary Chuck Hagel told reporters Thursday in Brussels, Belgium, where he was meeting with NATO defense ministers, that the United States was following the developments in and around Ukraine.
"Until we really know more details -- what's really happening there, who is in charge, I think the focus should be ... let's keep the tensions down. Let's see no provocative actions by anyone, any military," he said.
One concern is that with Russian troops out of their garrisons near Ukraine, they could be in a position to move swiftly across the border -- leaving little time for U.S. officials to try to mount diplomatic efforts to stop them, the official said.
But, for now, U.S. officials believe Putin is using the hastily ordered exercises only as a message to U.S. and Ukrainian officials that he has the ability to move his military into Ukraine to protect Russian interests if he chooses to, the official said.
Russia has significant interests in Ukraine.
Not only does it neighbor Ukraine, the two countries are major trading partners.
Many ethnic Russians live in Ukraine's east, and Russia has a major military base at Sevastopol, Ukraine.
Russian officials have complained that opposition figures who have taken control of Ukraine's government are threatening pro-Russian Ukrainians.
The United States is reviewing Russian tactics in its 2008 move into Georgia for clues about how Moscow might act in this instance.
In that incident, Russian forces fought troops from Georgia in a brief conflict that followed Russian promises to defend Russian citizens in the restive Georgian province of South Ossetia.
U.S. officials worry about a repeat of that incident, in which both sides perceived provocative actions and Russia finally moved in on a large scale.
Any military intervention by Russia would be a "grave mistake," Kerry warned Wednesday.
"For a country that has spoken out so frequently in the last year ... against foreign intervention in Libya, Syria, elsewhere, it would be important for them to heed those warnings as they think about options in the sovereign nation of Ukraine," he said.