Democrats on Monday demanded that President George Bush sideline the adviser.
One Democratic lawmaker said the intentional disclosure of a covert agent's identity amounted to an "act of treason".
Others urged Bush to sideline Rove by suspending his access to classified information and said the aide should "clear the air" by answering questions from Congress.
After publicly defending Rove for two years ago, the White House responded to a barrage of pointed questions on Monday by saying that it would not comment at the request of the prosecutors investigating who leaked the identify of the CIA agent, Valerie Plame.
Newsweek magazine reported on Sunday that Rove was one of the secret sources who spoke to Time magazine reporter Matt Cooper about Plame and her husband, former ambassador Joseph Wilson.
The Washington Post on Monday quoted Rove's lawyer as saying that his client did not mention Plame by name.
Rove is considered the architect
of Bush's election victories
Plame's name was leaked, her diplomat husband said, because of his criticism of the Bush administration's handling of the Iraq war.
Rove's lawyer was not immediately available to comment.
"The president should immediately suspend Karl Rove's security clearances and shut him down by shutting him out of classified meetings or discussions," said Senator Frank Lautenberg, a New Jersey Democrat.
Representative Henry Waxman, a California Democrat and the ranking minority member of the House Government Reform Committee, called for a congressional hearing of testimony from Rove, who is widely seen as the architect of Bush's election victories.
"The recent disclosures about Mr Rove's actions have such serious implications that we can no longer responsibly ignore them. The intentional disclosure of a covert CIA agent's identity would be an act of treason," Waxman said.
A US federal judge had ordered Cooper, along with New York Times reporter Judith Miller, to testify in the case and reveal their sources. Cooper avoided a jail sentence last week by agreeing to testify. Miller refused and was jailed.
Reticent White House
White House spokesman Scott McClellan, who was inundated with questions about Rove at his daily news briefing, declined to comment when asked whether Bush continued to have confidence in Rove.
"The president should immediately suspend Karl Rove's security clearances and shut him down by shutting him out of classified meetings or discussions"
"You're asking this question in the context of an ongoing investigation, and I would not read anything into it," McClellan said of his refusal to comment.
A grand jury investigation by special counsel Patrick Fitzgerald, a Justice Department prosecutor, is seeking to determine who in the Bush administration leaked Plame's name to the media in 2003 and whether any laws were violated.
In September and October 2003, McClellan rejected as "ridiculous" any suggestion that Rove was involved in the Plame leak.
When asked at an October 2003, briefing whether Rove and two other White House aides had ever told any reporter that Valerie Plame worked for the CIA, McClellan said: "I spoke with those individuals... and those individuals assured me they were
not involved in this... the leaking of classified information."