WASHINGTON — New York Times reporter Judith Miller has discovered notes of a conversation she had with Vice President Dick Cheney's chief of staff in June 2003 and has turned them over to the prosecutor investigating whether administration officials illegally leaked the identity of a covert CIA operative to the media, according to two sources familiar with the case.

Miller, 57, also has agreed to special prosecutor Patrick Fitzgerald's request that she meet with him Tuesday to answer additional questions, the sources said.

Miller testified before a grand jury Sept. 30 after spending 85 days in jail over her refusal to break a promise of confidentiality to her source. She changed her mind after the source, Cheney chief of staff I. Lewis "Scooter" Libby, urged her to answer Fitzgerald's questions about conversations they had July 8 and July 12 or 13, 2003.

Miller turned over some redacted notes to the prosecutor last week, and her attorneys asked her to re-examine others, according to a source close to Miller. She found some that involve discussions with Libby about the CIA operative's husband, Bush administration critic and former ambassador Joseph Wilson, the source said.

Miller attorney Robert Bennett declined to comment yesterday.

Fitzgerald has been trying to determine whether any administration official broke the law by leaking the identity of covert CIA operative Valerie Plame to the media in retaliation for her husband's criticism of the administration's justification for war with Iraq.

Wilson was sent by the CIA to check a claim that Iraq was trying to obtain material for nuclear weapons from Niger and found no evidence for it. He publicly criticized the administration on July 6, 2003, for asserting, in the run-up to the invasion, that Iraq was trying to obtain the material.

Eight days later, Plame's name and employment at the CIA were revealed in a column by Robert Novak.

But even as early as May 2003, according to administration sources, Cheney's staff was looking into Wilson, prompted by a May 6 New York Times column by Nicholas Kristof in which the mission to Niger was described without using Wilson's name.

By early June, several weeks before Libby is said to have known Plame's name, the State Department had prepared a memo on the Niger case that contained information on Plame in a section marked "(S)" for secret.

About that time, Libby knew about the trip's origins, although in an interview with The Washington Post at the time, he did not mention any role played by Wilson's wife.

Libby's attorney, Joseph Tate, did not return calls yesterday seeking comment.

Fitzgerald is wrapping up his investigation; the current grand jury's term expires Oct. 28.

He has asked White House deputy chief of staff Karl Rove to testify before the grand jury for a fourth time.