NEW YORK (AP) – Mayor Michael Bloomberg was publicly sworn in Sunday for another term and presented a rosy view of the city plus a sweeping promise of “finishing our unfinished work.”

During an outdoor City Hall ceremony on a chilly gray afternoon, Bloomberg took the oath of office and gave a short inaugural address that touched on the progress he believes he has made, while trying to set a more ambitious tone for the future.

“Now we have a choice to make,” Bloomberg said. “We could be content with what we have accomplished – and preserve our gains – or we can take our beloved city even further.”

The speech lacked the meatier specifics, which he has said he’s saving for the upcoming state of the city address. The 63-year-old mayor spoke in broad terms about his goals for economic development, schools and public safety – ideas he pushed during his re-election campaign.

With the city still stinging from the recent shooting deaths of two police officers, Bloomberg promised to draw national attention to gun control, which is emerging as a centerpiece cause for his second-term administration.

“We will not rest until we secure all the tools we need to protect New Yorkers from the scourge of illegal guns,” he said.

The now-seasoned mayor presented a much rosier view than the day he first stepped up to that podium four years ago, when the wounds of the Sept. 11 terrorist attack were still raw.

The billionaire businessman with no experience in politics took his first oath of office on New Year’s Day 2002, just months after the World Trade Center disaster. He inherited a brokenhearted city with a sinking economy and a school system plagued by a history of failure.

It was a day when “optimism seemed in jeopardy,” the Republican mayor said Sunday.

But things are turning around, he said. The crime rate continues to fall, school reforms are taking hold, the city has climbed out of fiscal despair and the fog of grief has lifted.

“True, the wounds we have suffered may never fully heal, but something else has endured,” Bloomberg said. “Something even more compelling, something even more powerful – our unity.”

It was a theme woven throughout his address and echoed by the program’s other speakers, including news celebrity Barbara Walters and entertainer John Lithgow.

William Thompson, a likely Democratic candidate for mayor in 2009, was sworn in for another term as comptroller on Sunday and said New York’s “light burns brighter than ever.”

Although the city’s $52 billion budget is balanced for this fiscal year, multibillion-dollar gaps lurk in the outer years. Budget watchdogs have questioned Bloomberg’s move to use up this year’s entire surplus instead of rolling it out to ease future pains.

The mayor briefly warned Sunday that now “is not the time to relax our vigilance,” but the fiscal woes that took up so much of his 2002 inaugural address were barely on the radar this year.

He has been drawing up a second-term agenda that includes opening more charter schools, building more affordable housing and designing economic redevelopment to replace “long twilights of blight and abandonment with the bright dawn of new parks, new homes and new hope.”

Echoing his 2002 speech, the mayor – a lifelong Democrat who changed parties just before his 2001 race – promised again to govern “without partisanship or prejudice.”

Four years ago, Bloomberg noted President Bush’s visit to ground zero and his promise of billions of dollars in aid, saying, “thank you, Mr. President, for all you have done and all that you will do to fulfill that explicit pledge.”

This year, Bloomberg made no mention of the president, who is unpopular in this heavily Democratic town. Bloomberg also sought to distance himself from Bush and national Republicans toward the end of his re-election campaign last year.

His two grown daughters and his mother, who turns 97 on Monday, were among the thousands of guests, many of whom huddled under blankets for the hourlong inauguration.

Entertainer Liza Minnelli helped heat things up and close the ceremony with a lurching rendition of “New York, New York,” at times pumping her fist in the air.

After the swearing in, guests headed to a celebration at the Emigrant Industrial Savings Bank building. As he did in 2002, Bloomberg paid for the party himself. It will be one of the final expenditures topping the $79 million he spent on his re-election.

AP-ES-01-01-06 1743EST