US Secretary of State Mike Pompeo said both he and Pentagon officials warned Russia not to offer bounties on US troops in Afghanistan.
Mr Pompeo discussed the exchange during an interview on Wednesday with Radio Free Europe and Radio Liberty.
"If the Russians are offering money to kill Americans or, for that matter, other Westerners as well, there will be an enormous price to pay. That's what I shared with Foreign Minister Lavrov," Mr Pompeo said. "I know our military has talked to their senior leaders, as well. We won't brook that. We won't tolerate that."
He said the Pentagon also issued warnings in the same vein.
The admission appears to undermine Donald Trump's messaging about the Russian bounty incident.
The president has at times claimed the entire story was a hoax, and at other times claimed the situation wasn't serious enough to warrant his consideration.
If Mr Pompeo spoke to the Russian foreign minister about the situation, it must have been serious enough to warrant the discussion and subsequent threat, and Mr Pompeo and the Pentagon must have seen it as more than a hoax.
Mr Trump said he did not bring the bounties up during a phone conversation he had with Russian President Vladmir Putin last month.
According to The New York Times, Mr Pomepo did not provide further details of his warnings to the Russians. It is unknown if the warnings were specific or vague, and he did not mention who from the Pentagon delivered its warning.
Shortly after The New York Times broke the Russia bounty story, US Army General Mark A Milley, the chairman of the Joint Chiefs of Staff, spoke to a Russian military officer, General Valery Gerasimov.
It is unusual for commanders to communicate directly in that method. It is unknown whether the officers discussed the Russian bounty scheme.
When Pentagon officials were asked if Mr Milley discussed bounties with his Russian counterpart, the Pentagon said that the conversations were kept private to allow the men the ability to speak freely.
The Russian bounty story exploded in June, when The New York Times reported - based on CIA analysis - that Russian military members were paying Taliban-affiliated fighters bounties for killing US troops in the region.