"We ought to get to the bottom of it so it can be evaluated, again, by the American people," Senate Judiciary Committee Chairman Arlen Specter said Sunday.
In a federal court filing last week, the prosecutor in the case said Cheney's former chief of staff, I. Lewis Libby, testified before a grand jury that he was authorized by Mr. Bush, through Cheney, to leak information from a classified document that detailed intelligence agencies' conclusions about weapons of mass destruction in Iraq.
A lawyer knowledgeable about the case said Saturday that Mr. Bush declassified sensitive intelligence in 2003 and authorized its public disclosure to rebut Iraq war critics, but he did not specifically direct that Libby be the one to disseminate the information.
Specter, R-Pa., did not dispute the White House claim that the president has the power to declassify secrets, reports CBS News correspondent Peter Maer.
"It may turn out that he had the authority to make the disclosures that were made but it was not the right way to go about it," Specter said.
But, he added, "it was not the right way to go about it because we ought not to have leaks in government."
He called for a detailed explanation of the leaks.
"I think that it is necessary for the president and vice president to tell the American people exactly what happened," Specter told "Fox News Sunday."
"I do say that there's been enough of a showing here with what's been filed of record in court that the president of the United States owes a specific explanation to the American people ... about exactly what he did," Specter said.
Libby faces trial, likely in January, on charges of perjury and obstruction of justice for allegedly lying to the grand jury and investigators about what he told reporters about CIA officer Valerie Plame.
Special Counsel Patrick Fitzgerald did not say in the filing that Cheney authorized Libby to leak Plame's identity, and Mr. Bush is not accused of doing anything illegal.