Reports initially stated that Trump did not learn about the bounties until March this year. "I stand ready to hold any members of your Administration accountable for their gross negligence in performing such a grave responsibility".
On Sunday, the president denied any knowledge about the bounties: "Everybody is denying it & there have not been many attacks on us".
Eight Republican Congress members attended a White House briefing led by Director of National Intelligence John Ratcliffe, White House Chief of Staff Mark Meadows and National Security Adviser Robert O'Brien on Monday.More news: Tupelo retires state flag to city museum
Trump's claim that he was unaware of Russian bounties on United States soldiers has been proven false. Lawmakers are pushing for an investigation into the accuracy of the intelligence.
White House Press Secretary Kayleigh McEnany did not answer when asked by reporters whether the information had been included in the president's written briefing, saying only that Mr Trump had not been "personally briefed".
Trump has denied knowing anything about the Russian bounties detailed in The New York Times report published online Friday. "And, in fact, there were dissenting opinions within the intelligence community, and it would not be elevated to the President until it was verified".
Several Democrats in the House of Representatives will hear details from the White House at 8 a.m. ET (1200 GMT) on Tuesday, an aide said, one day after the Trump administration briefed seven Republican lawmakers.
The Kremlin on Monday dismissed the reports as "lies".More news: Yeezy Lands 10-Year Deal with GAP
It was unclear how many American or coalition troops may have been targeted or killed under the Russian programme, according to a report in the Washington Post, but the intelligence stemmed from US military interrogations of captured fighters and was passed up from US Special Operations forces in Afghanistan. One of the officials said the item appeared in Mr. Trump's brief in late February; the other cited Feb. 27, specifically. On Sunday, Trump tweeted he and Vice President Mike Pence had not been briefed on the intelligence.
Late Monday, a White House official said Trump has been briefed on the intelligence behind reports of Russian bounties on US troops in Afghanistan and said the briefing took place "after the NY Times reported on unverified intelligence".
Trump's perceived refusal to act on the threats has been criticised by observers, including presumptive Democratic presidential nominee Joe Biden, who said during a Saturday town hall that Trump was "debasing himself" in front of Putin.
The unnamed officials cited by the New York Times' initial report said U.S. intelligence agencies had concluded months ago that a unit of Russia's GRU military intelligence agency had sought to destabilise its adversaries by covertly offering bounties for successful attacks on coalition forces.
The ODNI chief's statement comes shortly after White House spokesperson Kayleigh McEnany said that Trump had never received a briefing on the issue since there was never consensus among United States intelligence officials on whether the reports are credible.More news: Iran issues arrest warrant for Trump, asks Interpol to help