The White House is under pressure to explain how much the administration knew about allegations Russia offered the Taliban bounties to kill US troops.
Officials have insisted that President Donald Trump was not "personally" informed of the alleged plot in Afghanistan in 2019.
But reports say the president received a written briefing earlier this year.
There is concern that Mr Trump might have had access to information about threats to US forces but did not act.
The intelligence reportedly arrived amid US attempts to negotiate a peace deal to end the 19-year war in Afghanistan and while Mr Trump sought to improve relations with Russian President Vladimir Putin.
Reports by the New York Times, Washington Post and Wall Street Journal, quoting unnamed US officials, said a Russian military intelligence unit had offered Taliban-linked militants bounties to kill US troops in Afghanistan.
Twenty American troops died in Afghanistan in 2019, but the New York Times said it was not clear which deaths were under suspicion.
Russia denied the initial reports, while the Taliban said it had not made any deal with government intelligence.
The allegations come as Mr Trump seeks re-election in November.
Moscow maintains close links with the Taliban, as it sees the US involvement in Afghanistan winding down, the BBC's diplomatic correspondent Jonathan Marcus says.
He says Russia is also waging a "grey" or undeclared war against the West. Under President Vladimir Putin, the Kremlin has smarted from every perceived indignity suffered since the fall of the Soviet Union. It was US support for Afghan irregular fighters that contributed to Moscow's forced withdrawal from Afghanistan in the 1980s.
Pressed on the bounty claims, the White House spokeswoman on Tuesday insisted that Mr Trump was not briefed on the matter and claimed that "rogue intelligence officers" were behind the leak to the New York Times.
Asked to clarify if she meant members of the US intelligence community were going after the president, Kayleigh McEnany said: "It very possibly could be."
What are the new developments?
On Monday, the New York Times, citing two unnamed US officials, said the intelligence assessment had been included in the President's Daily Brief report - a written document with key government intelligence - in late February.
CNN and the Associated Press have also reported that the president received the intelligence in a written briefing earlier this year, without specifying when. Mr Trump is said to largely ignore the President's Daily Brief, relying more on oral briefings by intelligence officials a few times a week.
Ms McEnany said there was "no consensus within the intelligence community" about the assessment. But former intelligence officials told US media that, in previous administrations, claims of such importance would be reported to the president, even if the evidence had not been fully established.
She also defended Mr Trump when questioned whether the president reads his intelligence reports, saying he "does read and also consumes intelligence verbally".
"This president I'll tell you is the most informed person on planet earth when it comes to the threats that we face," she said.
Eight Republican members of Congress 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.
Some expressed alarm about the claims, calling for action against Russia and President Putin to be taken if the intelligence reports, currently under review, were confirmed.
Representatives Liz Cheney and Mac Thornberry, who is the top Republican on the House Armed Services Committee, said: "We believe it is important to vigorously pursue any information related to Russia or any other country targeting our forces."
Democrats were not included in the initial meeting, and they have been scheduled to take part in a briefing with White House officials on Tuesday.
The Associated Press reported that top officials in the White House were aware in early 2019 of the classified intelligence on the topic, and that the assessment had been included in at least one of President Trump's written daily briefings at the time.
What is the context?
The unnamed officials cited by the New York Times' initial report said US 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.
Islamist militants, or armed criminal elements closely associated with them, were believed to have collected the money.
The White House's National Security Council was said to have considered how to respond, including by imposing an escalating raft of sanctions against Russia.
President Trump was briefed on the reports in March, the New York Times reported. Mr Trump denied having been briefed, tweeting that neither he nor Vice-President Mike Pence had been told "about the so-called attacks on our troops in Afghanistan by Russians".
Sergei Zhirnov, a former agent of Russia's Foreign Intelligence Service (SVR), told BBC Russian that the GRU's actions could be a part of a larger game between Mr Putin and Mr Trump unfolding in the global arena.
"The GRU is a massive machine, which works towards making war. Putin likes to flex his muscles when there is no chance of retribution," said Mr Zhirnov.
The President, the Russians and the 'personal briefings'
Tara McKelvey, BBC White House correspondent
Did President Trump know about the alleged bounties for the killing of US troops?
One thing is clear: he has never paid much attention to CIA findings.
Unlike previous presidents, he does not receive written briefings. Instead intelligence analysts explain their findings in meetings, get-togethers that are scheduled sporadically.
When it comes to the Russians, though, the president pays attention. At a meeting with President Vladimir Putin in Helsinki in 2018, Mr Trump said he believed President Putin's claims that Moscow did not meddle in 2016 US elections, contrary to the findings of the US intelligence agencies.
The controversy over the Russian bounties is yet another reminder that Mr Trump's relationship with Mr Putin has been close. For Russians, this is a joy. For many in the US, it is deeply troubling.