CNN reports this, citing a statement by a Pentagon official and a National Security Council spokesman.
According to the key nuclear arms control treaty, the countries exchanged data on their nuclear forces.
Moscow's decision not to provide the information came after Vladimir Putin suspended Russia's participation in the START treaty.
It was the only bilateral treaty remaining between the world's two largest nuclear powers. The US strongly condemned the suspension of Russia's participation, which the NSC spokesman called legally invalid.
"Yesterday, we had a further interaction with Russia, pressing them on the upcoming end of the month, there is due a semiannual data exchange every six months, under the treaty, we exchange data on kind of high-level numbers," said John Plumb, Assistant Secretary of Defense for Space Policy, at a hearing of a House subcommittee.
He noted that Russia has refused, so the United States will not provide this information in response as part of a diplomatic countermeasure.
"We are going to continue to examine what diplomatic countermeasures [that] are appropriate. What we're trying to do, sir, is balance both responding to Russia's irresponsible behavior but to continue to demonstrate what we believe a responsible nuclear power’s action should be," Plumb said.
The NSC spokesman called the decision not to provide the data in response to Russia's actions a legitimate countermeasure aimed at encouraging Russia to return to compliance with the treaty, and noted that Russia's refusal to share the data would be a violation of the treaty, in addition to its existing violations of the START treaty.
On February 28, Russian President Vladimir Putin signed a decree on the temporary suspension of Russia's participation in the Strategic Arms Reduction Treaty.
The US Department of State emphasised that Russia's announced suspension of participation in the Strategic Arms Reduction Treaty is legally invalid.