President Bush has rejected lawmakers' demands for documents related to last year's firings of eight U.S. attorneys, invoking what is known as executive privilege.
But the White House says the president has not formally asserted executive privilege as to the testimony of former White House counsel Harriet Miers and former political director Sara Taylor.
White House spokesman Tony Snow says President Bush intends to assert the privilege over the testimony if Congress, as the spokesman put it, continues to "reject the president's offer of accommodation."
The White House gave the response Thursday, the deadline for answering subpoenas issued by the House and Senate Judiciary committees.
The lawmakers want to find out what role the White House played in the firings of the federal attorneys last year. Some Democrats alleged the firings were aimed at influencing the prosecution of corruption cases.
The White House has offered to have top aides be interviewed in closed-door sessions, but not under oath or with transcripts.
In a letter to the chairmen of the committees, White House counsel Fred Fielding said the president must be able to maintain confidential communications with his staff to ensure candid advice and open discussion among his advisors.
Thursday's developments come one day after Senate Judiciary Committee chairman Patrick Leahy sent subpoenas to the White House, Vice President Dick Cheney's office, the Justice Department and the National Security Council for material on a controversial domestic wiretapping program.
The Bush administration has three weeks to respond to the subpoenas.
The program allowed the government to monitor communications between people in the United States and suspected terrorists abroad - without a court warrant.
President Bush has accused Democrats of engaging in what he calls "pure political theater."
Some information for this report was provided by AP and Reuters.