Mayor Giuliani said yesterday that if he is elected president in 2008, he will use the CompStat crime measurement system, employed during his eight years at City Hall, to improve the performance of federal agencies.

“If we get elected president,” Mr. Giuliani said at a news conference yesterday in Midtown, “it will turn around the federal government just as well as it turned around New York City.”

The Giuliani administration implemented CompStat in the 1990s to track crime statistics and hold police commanders accountable for them.

The system is widely credited with helping to reduce city crime and was later expanded to other areas, including tracking jail violence and welfare-to-work progress.

The former mayor yesterday repeatedly credited his first police commissioner, William Bratton, with helping to develop CompStat.

The two men were estranged for years, with Mr. Bratton, now the police chief in Los Angeles, griping that Mr. Giuliani took credit for a system others also pioneered. The two have since reconciled.

CompStat’s success helped lead a former FBI agent, prosecutor, judge, and bureau director, Louis Freeh, yesterday to endorse Mr. Giuliani, whom he said he has known for 25 years, beginning when the two worked together in the Manhattan federal prosecutor’s office.

“[What] Rudy put into place, the CompStat program, it was a very simple formula: We can’t manage what we can’t measure,” Mr. Freeh said.

Also yesterday, Mr. Giuliani said he welcomed the news that a former senator from Tennessee, Fred Thompson, is taking the first official steps of a possible run for president.

“There are now 10 Republican candidates. If there are 11 or 12, it’s not going to change things very much,” Mr. Giuliani said. “I’m not running against anybody.”