One of President Bush’s closest advisers, Karl Rove, will soon make a fourth appearance before a federal grand jury investigating how the identity of a CIA operative was leaked to the press, Mr. Rove’s attorney said yesterday.

The lawyer, Robert Luskin, said in an interview that the agreement for further testimony was a response to an offer he extended in July to the special prosecutor pursuing the case, Patrick Fitzgerald.

“I told him that Karl’s offer to cooperate was continuing in nature,” Mr. Luskin said. “He contacted me at the end of last week and told me he’d like to accept that offer.”

Mr. Luskin denied that Mr. Fitzgerald had given any indication that Mr. Rove is a target of the investigation. “He told me he hasn’t made any decision about whether to charge Mr. Rove. He absolutely did not tell me he was a target.”

Mr. Fitzgerald is believed to be concluding his inquiry into the unmasking of the CIA employee, Valerie Plame, in July 2003. Last week, a New York Times reporter who spent nearly three months in jail for failing to testify in the investigation, Judith Miller, was released after another top White House aide, I. Lewis Libby, authorized her to speak about confidential conversations they had.

Efforts to reach a spokesman for Mr. Fitzgerald yesterday were unsuccessful. In court appearances, the Chicago based prosecutor has said the probe is examining whether Ms. Plame’s identity was disclosed in retaliation for criticism her husband, Joseph Wilson, leveled at President Bush.

A Manhattan defense attorney, Joshua Dratel, said the additional appearance by Mr. Rove could signal that he wants to correct something he said in earlier testimony. “Oftentimes, repeated grand jury appearances means there is something the examine wants to clarify or the witness wants to clarify,” Mr. Dratel said. He noted that a witness cannot be charged with perjury if he corrects his testimony before the proceeding concludes. “The perjury statute does have a fail-safe recantation provision,” he said. Mr. Luskin said Mr. Rove was not seeking to “correct or otherwise modify his testimony.”

While the White House insisted in 2003 that Mr. Libby and Mr. Rove were not involved in the leak, a Time magazine reporter, Matthew Cooper, said earlier this year that he discussed the sensitive issue with both men before Ms. Plame’s name became public.

According to legal experts, Mr. Fitzgerald is likely to have difficulty proving the leak of Ms. Plame’s identity was a crime. However, lawyers who know Mr. Fitzgerald suspect that he may bring an ancillary charge, such as obstruction of justice, perjury, or conspiracy.

“To the extent that any charges are going to be brought, that’s where I’d be looking, not to the underlying offense,” a former deputy attorney general, Eric Holder, said.

Mr. Dratel, who represented a client prosecuted by Mr. Fitzgerald for perjury and conspiracy in connection with bombings of American embassies in Africa in 1998, said the prosecutor took offense when witnesses said things he considered false. “Pat is not a guy who likes to be lied to. He takes it personally,” the defense lawyer said.

Mr. Fitzgerald is also known to be stern with those who fail to cooperate with an inquiry. “Even the Judith Miller thing, there was a certain level of indignance about it,” Mr. Dratel said.

Mr. Rove’s impending return to the grand jury was first reported by the Associated Press.