"I have real questions about this. I think the timeline has to be looked at. I'm suggesting there's a lot of unanswered questions," Rep. Peter T. King (R-N.Y.) said on CNN's "State of the Union."
King, the House Homeland Security Committee chairman, said the current timeline "just doesn't add up."
Republicans want Petraeus to testify as a civilian. King called him "an absolutely necessary witness." Sen. Saxby Chambliss (R-Ga.), vice chairman of the Senate Intelligence Committee, said he "would not rule out" calling Petraeus.
A host of questions remains about the scandal that upended the career of Petraeus, one of the most influential national security officials of his generation. It's not clear, for example, whether the FBI obtained a warrant to read Petraeus' email, or merely reviewed messages he sent that resided in Broadwell's account.
It's also unclear why the FBI did not notify the White House that the CIA director had been caught up in an investigation. Doug Heye, a spokesman for Rep. Eric Cantor (R-Va.), said Cantor had a conversation last month with an FBI whistle-blower about the affair and potential "national security concerns."
But when Cantor raised the matter with the FBI, Heye said, he was told that the agency could neither confirm nor deny any investigation, and that all necessary steps were being taken to ensure no confidential information was at risk.
U.S. officials have said there are no indications that Petraeus improperly shared classified information with Broadwell. Although some observers have suggested that a CIA director carrying on an affair would be subject to blackmail, former CIA officials say extramarital affairs are common at all levels of the agency and typically are viewed as a security problem only if the officer is involved with a foreigner or someone who poses a risk.