House Speaker Nancy Pelosi on Monday requested an inter-agency brief for all members of the House immediately on this issue, reports Xinhua news agency.
"The questions that arise are: was the President briefed, and if not, why not, and why was Congress not briefed. Congress and the country need answers now," Pelosi wrote in her letter to Director of National Intelligence John Ratcliffe and CIA Director Gina Haspel.
"The administration's disturbing silence and inaction endanger the lives of our troops and our coalition partners," she added.
Republican Senator Jim Inhofe, chairman of the Senate Armed Services Committee, tweeted on Monday: "We need answers. I have asked the administration to share what it knows, and I expect to know more in the coming days."
President Donald Trump said late Sunday denied he was briefed on the issue since the intelligence was not credible.
"Possibly another fabricated Russia Hoax, maybe by the Fake News @nytimesbooks, wanting to make Republicans look bad," Trump tweeted.
In a report on June 26, The New York Times said that Trump had been briefed that Russian intelligence units secretly offered bounties to Taliban-related militants for killing coalition forces in Afghanistan during US-Taliban peace talks.
The report also said the National Security Council discussed this issue at an inter-agency meeting in late March, while the White House thus far has not taken any actions to respond.
The Washington Post reported on Sunday piece that Russian bounties offered to Taliban-linked militants were believed to have led to the deaths of several US soldiers.
Twenty-two American troops were killed in Afghanistan last year, which marked the deadliest year for US service members in the South Asian country since 2014.
The US invaded Afghanistan in 2001, and the death toll of American service members has surpassed 2,400.
Trump has long complained about the endlessness of the war and sought a full withdrawal from Afghanistan.
The US and the Taliban signed a peace deal in late February, in which Washington said it would reduce its forces in Afghanistan to 8,600 within 135 days.
The agreement also called for the full withdrawal of the US military by May 2021 if the Taliban meets the conditions of the deal, including severing ties with terrorist groups.