WOLFEBORO, N.H. — Mayor Giuliani, using his strongest words yet to describe the allegations that Governor Spitzer’s office employed the state police to improperly scrutinize the Senate majority leader, Joseph Bruno, is calling upon Attorney General Cuomo to conduct a full inquiry into the matter with subpoena power.

While Mr. Giuliani did not specifically call for Mr. Cuomo to be made a “special prosecutor,” as some Senate Republicans want, the statements by the former U.S. attorney for the Southern District of New York appear to echo their request for a complete probe backed by subpoena power.

“These are very serious allegations. We don’t know if they’re true or not — how much he knew, how much they knew. If that’s what they were doing to Joe Bruno, siccing the state police on him, that is a very serious allegation,” Mr. Giuliani said, cautioning that “nobody should draw a conclusion before the investigation is over.”

Mr. Giuliani praised the work of Mr. Cuomo and said he ought to be more fully empowered to investigate the matter. Mr. Cuomo’s office last week issued a report into the alleged misuse of the state police, concluding “that no surveillance occurred, but that serious issues have been raised about the use of the State Police to collect, create, and produce to the Governor’s Office documents and information regarding Senator Bruno’s travel.” Two aides to Mr. Spitzer, Darren Dopp, the communications director, and Richard Baum, the secretary to the governor, declined to be interviewed voluntarily for Mr. Cuomo’s investigation. The New York Sun reported yesterday that the inspector general’s office conducted its own investigation but did not interview the men despite having the power of subpoena.

“I think the attorney general could conduct the investigation fully and fairly if he was able to subpoena people, which he wasn’t able to do in the first round of the investigation,” Mr. Giuliani said. “I think Attorney General Cuomo did every thing that he could. I think it was quite remarkable. I think it was quite independent, the review that he did, and fair and even fair to the governor in that it drew no conclusions, it just raised the questions. I think now it’s time for the conclusions.”

A spokeswoman for the governor, Christine Anderson, rejected Mr. Giuliani’s call for an investigation with subpoena power.

“The attorney general concluded its report. Even Senator Bruno deemed the report fair, thorough, and independent. The report found no illegality and no surveillance,” she said. As far as a further investigation by a special prosecutor, she said: “Given that the attorney general and the inspector general have closed their investigations and found no violations of the law, the appointment of a special prosecutor is unnecessary.”

A spokesman for Mr. Cuomo’s office, Jeffrey Lerner, had no comment on Mr. Giuliani’s suggestion and said of the possibility of a special prosecutor: “It is inappropriate for us to comment on this matter. The findings of our report speak for themselves.”

Mr. Giuliani spoke with sympathy about Mr. Bruno, who endorsed his presidential campaign in May. “Joe is a good friend of mine, and he’s someone I’ve worked with for a very long time,” he said.

“I’ve always found Joe Bruno to be somebody, who kept his word, whether you agree with him, whether you disagree with him, to see this happen to him is personally very, very disturbing, to see the state police focused on him in a way where the State Police are being used for political purposes.”

The former New York mayor said a complete investigation was needed for Mr. Spitzer’s sake as well. “We don’t know exactly who did that, who ordered it. I don’t think it’s fair to lay it at the governor’s feet until you look at it. Maybe it will turn out that the governor didn’t know about it. That doubt should be removed.”