Mayor Bloomberg attempted to speed up the stalled development at the World Trade Center site, called for public employees to contribute to their health care costs, and proposed a Megan’s Law-style registry to track the addresses of individuals convicted of gun crimes during his annual State of the City speech yesterday.

Signaling his intention to wrestle for more control over the redevelopment of Lower Manhattan, the mayor asked the main leaseholder at ground zero, Larry Silverstein, to relinquish two buildings on the site to the Port Authority of New York and New Jersey so that development at various buildings can move forward simultaneously.

“We cannot allow the Trade Center to be a construction site for the next 15 years,” the mayor told about 825 elected officials and community leaders at the Snug Harbor Cultural Center on Staten Island.

The mayor said Mr. Silverstein should turnover Towers 3 and 4 to the Port Authority. A spokesman for the Port Authority said lease negotiations with Mr. Silverstein have been under way for some time and that Governor Pataki has set a March deadline. Mr. Silverstein’s firm said it is ready to begin building all of its towers, but that the government has not yet prepared the site for construction.

“As City Hall is well aware, the Port Authority has not yet begun this key preparation work, including excavating the sites and building a protective slurry wall,” the director of World Trade Center development for Mr. Silverstein, Janno Lieber, said.

During his 52-minute speech, the mayor touched on dozens of issues, including job creation, teacher training programs, initiatives to address poverty in places such as the South Bronx, banning gift-giving by lobbyists to politicians, the expansion of DNA use in crime solving, and increasing the number of charter schools.

Mr. Bloomberg also made it clear that he is preparing to take on the city’s skyrocketing pension and health care costs, which have contributed to a structural imbalance in the city’s $50 billion budget. He vowed to work with labor leaders to reach contract agreements that include health care contributions from public employees, and he said “pension modifications” are necessary.

The pronouncement came as music to the ears of some in the audience and drew criticism from others.

The president of the United Federation of Teachers, Randi Weingarten, said she was “surprised” that the may or chose to highlight the issue in such a high-profile setting when transit workers just rejected a contract that called for union members to contribute to their health care coverage.

“There are lots of things that the New York City workforce has done to help the city, but in a period of unprecedented prosperity where the mayor is looking to increase health care for others, he can’t at the same time look to decrease it and roll it back for the hardworking New York City workforce,” Ms. Weingarten told reporters after the speech.

The city’s comptroller, William Thompson Jr., who has been named as possible mayoral candidate for 2009 when Mr. Bloomberg is termed out of office, had nothing but praise for the mayor and said the city “does have growing gaps” in the budget.

When asked whether the mayor’s pledge to push for extending $400 property tax rebates for the duration of his term should be replaced by lowering the property tax rate, Mr. Thompson said the government should “probably take a look” at a slightly lower rate.

Rep. Anthony Weiner, who was campaigning against Mr. Bloomberg just a few months ago, said: “If there is a person and a time to take on these big structural problems, Mike Bloomberg is the person and this is the time.”

He continued: “Obviously it’s going take a great deal of discussion and debate and there’s going to be opposition to finding some cures for these problems, but you got to do it. This is an unsustainable arch we’re on with pension costs, health care costs, and debt costs.”

The new speaker of the City Council, Christine Quinn, said she was generally pleased with the speech but that the depth of Mr. Bloomberg’s commitment to things like AIDS and health care enrollment will be more evident only next week, when he unveils his preliminary budget. She indicated that she would support the mayor’s proposed ban on gifts to politicians from lobbyists, which the council will presumably have a say in.

Mr. Bloomberg also offered more specifics about gun control, an issue he has pushed aggressively in recent weeks. He said that in addition to pushing Albany to create a gun offenders’ registry, he will push the state to increase penalties for illegal possession of a loaded gun and work with the council to enact a law limiting to one the number of guns an individual can purchase every three months.

Council Member Charles Barron, one of the council’s most liberal members, and Council Member Dennis Gallagher, one of only three Republicans in the 51-member body, had different takes on the speech. Mr. Barron chided the mayor for addressing poverty only four years after taking office and said the speech had “a lot of flowery rhetoric.” He said he wanted to “see whether the budget money matched all the rhetoric.”

Mr. Gallagher said he was more concerned about how the city will pay for all of the new programs Mr. Bloomberg announced. “I hope that there’s enough to fund these things without having to burden middle class taxpayers, but I’m skeptical,” he said.