Rep. John Conyers, D-Mich., said the ongoing legal battle to get Rove and other former Bush administration aides to testify may have success with a new president in the White House.
Former President George W. Bush upheld Rove and two other senior aides who asserted they did not have to testify before Congress about their actions in the White House.
The legal dispute between the executive and legislative branches of government is before a federal appeals court.
Rove's lawyer, Robert Luskin, said his client was only following Bush's orders and never asserted a personal claim that he could disobey a congressional subpoena. Luskin added that if the Obama administration no longer asserts a legal claim against Rove testifying, "we will do our best to work it out with the new president."
"This is not Mr. Rove's dispute," Luskin said.
The subpoena commanded Rove to appear on Feb. 2 for a deposition on the U.S. attorney firings and the prosecution of former Alabama Gov. Don Siegelman, a Democrat.
Former Attorney General Michael Mukasey named a special prosecutor in September to investigate whether former Attorney General Alberto Gonzales, other Bush administration officials or Republicans in Congress should face criminal charges in the firings of the U.S. attorneys.
The inquiry followed the recommendation of internal Justice Department investigators who concluded that, despite administration denials, political considerations played a part in the firings of as many as four of the federal prosecutors. Conyers wants to know what role Rove played in the dismissals.
Siegelman has alleged his prosecution was pushed by Republicans, including Rove. The former governor was convicted on bribery and other charges and was sentenced to more than seven years in prison. He was released early, when a federal appeals court ruled his appeal raised "substantial questions."
Conyers said in a statement that times have changed.
He said Bush's position of "absolute immunity" was "rejected by U.S. District Judge John Bates and President Obama has previously dismissed the claim as 'completely misguided,"' Conyers said.
"I have said many times that I will carry this investigation forward to its conclusion, whether in Congress or in court, and today's action is an important step along the way.
"Change has come to Washington, and I hope Karl Rove is ready for it. After two years of stonewalling, it's time for him to talk."
Last July, Bates rejected Bush's contention that senior White House advisers are immune from subpoenas, siding with Congress' power to investigate the executive branch.
Conyers also has sought testimony from former White House counsel Harriet Miers, and ex-White House chief of staff Josh Bolten - although only Rove was named in the new subpoena.