New York Mayor Michael Bloomberg started his four-year term of office Wednesday morning with appearances on the morning news shows and a meeting with city union leaders to hammer out work contracts that have been stalled for more than a year.

Taking a softer tone than that of his predecessor Rudolph Giuliani, Bloomberg said he will use his personal style of business to reach a deal with union officials from the police, fire, and education sectors of the civil service.

"I tend to sit down and talk with people and break bread with people and try to develop relationships. That's always stood me in good stead in the past and that's the way to go forward," he said on CBS's The Early Show.

But reaching a deal may require some creative solutions since the city is in a tough financial situation following the Sept. 11 terror attacks, Bloomberg said.

The 59-year-old political novice enters office faced with three consecutive years of budget gaps greater than $3 billion, an underperforming 1.1-million student school system and a citizenry still jittery from the Sept. 11 terrorist attack, subsequent anthrax attacks and countless false alarms.

"I think we're going to have to find some ways whether it is payment later on for services now, or adjusting pensions so that people still get their monies," Bloomberg said. He said it may be necessary to cut the size of the uniformed services through attrition.

He also reiterated the promise he made at his New Year's Day inauguration to cut his own staff by 20 percent and urged other city departments to make similar sacrifices.  The challenge was not met well on Tuesday when scattered boos greeted the proposal from the politically connected audience outside City Hall.

On Wednesday, Bloomberg said he wanted to erect a memorial at the World Trade Center site for the nearly 3,000 people lost in the Sept. 11 attack. He also wants some of the 16-acre site to be used for offices, schools or housing.

Bloomberg said he would follow through on his campaign promises to make education and affordable housing top priorities, and he suggested he may find room in the budget for Giuliani's $1.6 billion plan to build new baseball stadiums for the New York Mets and New York Yankees.

Bloomberg has taken three oaths of office to become mayor, the first on Monday afternoon before the city clerk. The second swearing in was an honorary event by Giuliani done in the middle of Times Square just minutes after the crystal ball dropped to signal the beginning of 2002.  An official ceremony was performed by chief judge of New York State, Judith Kaye on Tuesday.

In that noontime ceremony, a giant American flag unfurled behind the podium after Bloomberg stepped outside from the doors of City Hall to become the city's 108th mayor. Bloomberg wore an American flag pin on the lapel of his dark overcoat in the freezing weather.

More than 4,000 invited guests braved the weather for the inaugural, including Democratic Sens. Hillary Clinton and Chuck Schumer and former mayors David Dinkins and Ed Koch. Bette Midler sang the national anthem and several religious leaders offered prayers. Jazz musician Wynton Marsalis, who played the trumpet, could be seen during the ceremony doing lip exercises before performing in the frigid weather.

Bloomberg, who has never held public office, made his fortune on Wall Street and from the Bloomberg L.P. media company.  He spent $69 million of his own money in his bid to succeed Giuliani. Bloomberg has said he would take a salary of $1 a year rather than the $195,000 pay.

Giuliani, who could not run for a third term because of term limits, will open Giuliani Partners, a consulting firm that will have a strategic partnership with accounting firm Ernst & Young.  He will employ several of his top aides.

The Associated Press contributed to this report.