Moscow has voiced concern over an “unprecedented” increase in US and Nato military activity near Russian borders, amid an escalating crisis in Ukraine.
Russia’s Defence Minister Sergei Shoigu expressed the concerns in a phone call to US counterpart Chuck Hagel.
But the US said Mr Shoigu also pledged Russia would not invade Ukraine.
The US says it deployed extra troops in eastern Europe to reassure Nato allies. It has also imposed new sanctions on Russia over its actions in Ukraine.
The sanctions target seven Russian individuals and 17 companies which Washington says are linked to President Vladimir Putin’s “inner circle”.
The European Union is also imposing new sanctions on 15 people who will be named on Tuesday.
In a statement, Mr Shoigu said he had a “candid” hour-long phone call with his American counterpart.
Mr Shoigu stressed that US and Nato military activity in eastern Europe was accompanied by “provocative” statements about the need to “contain” Russia.
Mr Shoigu also announced that Russian troops had returned to their “permanent positions” after conducting military exercises on the border with Ukraine.
But he did not say whether the overall number of Russian troops deployed in the region – said to be around 40,000 – had been reduced.
The Pentagon said Mr Shoigu had given “assurances that Moscow has no plans to invade Ukraine”.
It said Mr Hagel had warned that Russia’s continued aggression would result in more diplomatic and economic pressure.
He also called on Moscow to help secure the release of seven military observers linked to the Organization for Security and Co-operation in Europe seized by pro-Russian gunmen in the town of Sloviansk last week.
Some 40 people, including journalists, pro-Kiev activists and three members of Ukraine’s security service are being held there.
The Russian ambassador to the OSCE, Andrei Kelin, earlier said Moscow was taking “steps” to secure the observers’ release.
The US and EU first imposed visa bans and asset freezes on a number of senior Russian officials and companies after Moscow annexed Crimea from Ukraine last month.
On Monday, Washington added to its sanctions list “in response to Russia’s continued illegal intervention in Ukraine and provocative acts that undermine Ukraine’s democracy”.
Among the individuals named are Igor Sechin, head of state oil giant Rosneft, and Alexei Pushkov, chairman of the committee of international affairs of Russia’s lower house of parliament.
The US accused Russia of “doing nothing to meet the commitments it made” at a meeting with Ukraine, the US and EU in Geneva on 17 April, which it said had included refraining from violence or provocative acts.
Russian Deputy Foreign Minister Sergei Ryabkov said Moscow’s response would be “painful for Washington”
Meanwhile, a US journalist who was kidnapped and held hostage for several days last week by pro-Russian activists has been speaking to the BBC.
Simon Ostrovsky said he was pulled out of his car at a checkpoint in Sloviansk.
“I was separated from my other colleagues and taken down into the basement, blindfolded. I had my hands tied behind my back. I was thrown on the floor and beaten up and held there for the next three days,” he said.
But he said he was unable to confirm any of those involved were from Russia.