Mayor William Green, a political boss' son who was elected mayor of Philadelphia in 1979 as a reformer, announced yesterday that he would not seek a second term next year.

Green, 44, said he wanted a respite from public life so he could spend more time with his family, but he made it clear he still harbors political ambitions.

"I would certainly not rule out running for public office again," said Green, whose three-year tenure has been marked by a steady if unspectacular improvement of some of the city's budget and racial problems.

The surprise press conference at City Hall yesterday immediately fueled speculation that former mayor Frank L. Rizzo, the one-time policeman who ruled Philadelphia with an iron fist for eight swashbuckling and racially charged years in the 1970s, would try for a comeback.

Rizzo supporters yesterday announced creation of a campaign committee and scheduled their first fund-raiser for next month.

Rizzo, 62, who has stayed idle since he lost a bid in 1978 to eliminate a two-term limit on the mayor's office, said yesterday that he wished Green and his family well.

The other likely entrant into the 1983 mayoralty race is W. Wilson Goode, who holds the post of city managing director, the highest appointive job in city government. Goode, who is black, has been considering the mayor's race all year, but had ruled out running against Green, the man who appointed him.

Other possible candidates are City Controller Thomas Leonard, who was once allied with the Rizzo wing of the Democratic Party but who has since developed a more independent base, and City District Attorney Edward Rendell, who was elected to a second term in a landslide last year.

Friends have long remarked that Green maintained a love-hate relationship with the mayor's job. He grew up at the knee of a father who served in Congress and ran the Democratic Party until his death in 1963. Politics was in young Green's blood and he told friends he always considered the mayor's job his destiny.

He was elected in a campaign that promised a cooling of racial tensions and a reform of what were alleged to be the patronage abuses and lax budget policies of the Rizzo era.

During his three-year tenure, Green adopted a program of fiscal austerity that brought him his share of battles with all the elements of the urban stew -- unions, minorities, teachers, municipal employes and white ethnics. And yet at the time of yesterday's announcement, he was enjoying what most observers believed was a political upswing.

He had engineered a three-year teachers' contract last summer, and the appointment this fall of the city's first black--and female -- school superintendent in a system that is more than 70 percent nonwhite was widely praised.

Through the usual ups and downs, say friends, Green chafed at the relentless pressures and fishbowl lifestyle of his office. Moreover, his decision-making style as a public servant -- for 12 years in Congress before he ran for mayor -- was one of extreme deliberateness, or "analysis paralysis," as one aide dubbed it. It was a style often out of sync with the fast-paced demands of running a city, aides said.

Few close to him doubted that personal considerations were paramount in his decision. Green's fourth child, a daughter, was born last month, and his wife Patricia was known to have called for his getting out.

Political advisers said they believe he could have easily won reelection next year, but that he would be better positioned to seek other offices as an ex-mayor.

The office Green is said to be eyeing is the U.S. Senate in 1986, when he would be squaring off against another Philadelphian, Republican Sen. Arlen Specter.

Green has run for the Senate once before, in 1976, when he lost to Republican H. John Heinz.