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Mr. Cuomo, a Democrat, had two emotional fulcrums in his sprawling 78-minute address: gun violence and Hurricane Sandy. But most of the speech was devoted to an onslaught of proposals favored by the left wing of his party.

He proposed increasing the minimum wage to $8.75 an hour from $7.25 an hour, public financing of elections, tougher greenhouse gas standards, solar jobs programs, a $1 billion affordable housing initiative, grants for schools that extend school days and a 10-point women's rights program that garnered loud applause for its provisions strengthening abortion rights laws and enacting equal pay legislation.

"We are a community based on progressive principles," the governor said, in a speech to several hundred lawmakers and guests at an auditorium in the Capitol complex. "We must remain that progressive capital of the nation."

How the state would pay for any new programs was not clear. The governor is to introduce his budget this month, but until Congress decides how much aid to send to New York to defray the costs of rebuilding after Hurricane Sandy, the state's financial picture will be clouded.

The governor promised not to raise taxes. He has made similar promises in the past, but then agreed to support a new higher tax bracket for the state's highest earners. And he said he would continue to push for a referendum in November allowing an expansion of casino gambling, describing casinos as vehicles for improving the upstate economy. He said that, at first, he would allow as many as three full-scale casinos upstate, and none in New York City, in an effort to lure tourists to travel to economically struggling areas.

Overall, the speech served to reposition the governor, who has faced criticism from the left wing of his party for paying too little attention to their concerns. Liberals praised the governor in 2011 for persuading lawmakers to pass same-sex marriage legislation. But his first two years in office focused on a centrist fiscal policy that included a cap on property tax increases, steep spending cuts and contentious negotiations with unions that resulted in a cut to the pension benefits of future state employees.

Now Mr. Cuomo, who is considered, at least in New York, a presidential contender for 2016, is emphasizing proposals — some new and some he has suggested in the past — that cheer his Democratic base. Some contentious issues, like hydraulic fracturing, which is opposed by the left, were notably absent from his speech. Those attending the speech passed protesters of fracking in the largest demonstration before a State of the State address in several years.

Few advocacy groups on the left found issues they could not applaud. Environmental Advocates of New York said Mr. Cuomo "showed true leadership" in his comments on climate change. Andrea Miller, president of Naral Pro-Choice New York, said of his proposed women's initiatives, "He heard the call and is a true leader."

Bob Master, director of legislative action at the Communications Workers of America, said, "To the extent he's using this speech to appeal to the liberal primary electorate, doing something meaningful on public financing would be a big achievement."

Republicans also saw the trend, but bemoaned it. Assemblyman Steve Katz, a Hudson Valley Republican, called the speech "a sharp veer to the left offering big government solutions for all problems."

Even the cover of a 300-page book that accompanied the speech was something of a kitchen sink — an odd tableau that superimposed a stark image of Breezy Point, the Queens neighborhood devastated by Hurricane Sandy, on the front lawn of the Capitol building, with a new model of the Tappan Zee Bridge soaring overhead.

The governor gave some of his most impassioned remarks to date on guns, a cause he has voiced support for in the past but has not made a legislative priority. Mr. Cuomo's legislative agenda was clearly upended by the recent mass shooting in Newtown, Conn., and the killings of two firefighters in Webster, N.Y. "End the madness now," he said Wednesday.

"Forget the extremists — it's simple," the governor added, to a burst of applause. "No one hunts with an assault rifle. No one needs 10 bullets to kill a deer."

The governor also continued to use Hurricane Sandy as a reason to talk about global warming.

"Climate change is real," he said. "It is denial to say each of these situations is a once-in-a-lifetime. There is a 100-year flood every two years now. It is inarguable that the sea is warmer and there is a changing weather pattern, and the time to act is now."

Among his proposals were a bailout fund for homeowners who want to move out of flood-prone regions, and aid for building homes that can better withstand floods — ideas that are contingent on how much federal aid comes through. He also called for measures to better protect subways, public utilities, the fuel delivery system and New York Harbor.

And he excoriated Washington for waiting so long to provide New York and New Jersey with federal storm aid.

"That is just too little and it is too late, and it has nothing to do with the way Congress has acted in the past," he said. "This has long been established, that in the face of a disaster, the national government comes in to help."

"Remember New York," he added, "because New York will not forget, I promise you."