WASHINGTON (CNN) -- The White House will allow the president's top political adviser, Karl Rove, and former White House counsel Harriet Miers to be interviewed by congressional committees investigating how the firing of several U.S. attorneys was handled, but they will not testify under oath in the matter.

The announcement came after current White House counsel Fred Fielding met with members of the heads of the House and Senate Judiciary committees, who had considered using subpoenas to force Rove, Miers and their two deputies to reveal what they knew about the reasons behind the firings of at least seven U.S. attorneys.(Read: Fielding's letter to congressional committee leaders regarding Rove, Miers [PDF])

Sen. Chuck Schumer, D-New York, told reporters after the meeting with Fielding that the offer from the White House "is incomplete."

"We would be able to interview the four people we requested ... but only in private, not under oath and with no transcript," he said.

Although Fielding indicated that he was not prepared to negotiate in the matter, Schumer said lawmakers would try to get tougher requirements for the interviews.

"He wanted this to be a conversation rather than a hearing, but let's have a conversation under oath and with a transcript," Schumer said.

Schumer and House Judiciary Committee head Rep. John Conyers said both committees will move forward to approve the use of subpoenas to get White House officials to testify.That would not mean that subpoenas would be issued immediately, only that the committees would be able to use them.