ALBANY – Gov. Andrew M. Cuomo took a hard left turn Wednesday in his annual State of the State address – one reminiscent of those his liberal father regaled New York with for 12 years – calling for sharp restrictions on guns, a larger hike in the minimum wage than even Assembly Democrats had sought, and relaxation of marijuana-possession laws.

He also voiced support for equal-pay provisions for women and expensive new housing programs for low-income residents.

Cuomo, starting his third year in office, again focused on job-creation efforts, with pitches that include new tax breaks for startup companies and money for high-technology clusters, but saved many of his rhetorical flourishes for what he called his “progressive”’ agenda for the 2013 legislative session.

“End the madness now,” he shouted in pushing for new bans on assault weapons and confiscation of guns from people deemed by mental health professionals to be a threat.

“It’s not a man’s world in New York,” Cuomo said in promoting a 10-point “equality for women” agenda that includes broader abortion-access protections and a pay-equity statute for women in the workforce.

Reactions to the speech told the story of a shifting governor, who has alienated many liberal groups for two years but now, with a re-election campaign looming next year and his eyes on a possible White House run in 2016, is leaning leftward.

“Clearly, it was not only a speech about New York. It was a speech way past New York heading to Washington. And he circled back to his liberal roots, went home to meet his dad,” Michael R. Long, the state Conservative Party chairman, said of the governor and his father, former Gov. Mario M. Cuomo.

“He certainly has moved to the progressive left,” added Sen. Dean G. Skelos, R-Rockville Centre, co-leader of the State Senate.

Then there was Assembly Speaker Sheldon Silver, D-Manhattan, who has seen Cuomo move from ignoring to now embracing many Assembly Democratic plans, including a hike in the minimum wage. “I thought it was a great speech, probably his best of the three that he’s given,” Silver said.

While the governor talked often of the need to help the deteriorating upstate job-creation situation – which he called “sad and troubling” – his proposals this year were not as bold as ones he pushed in his previous two State of the State addresses, such as last year’s $1 billion for Buffalo job-creation efforts. This time, the plans were less expensive for the state, such as a $5 million annual ad campaign to boost upstate regions.

The governor said his plans for high-tech clusters, and cuts in unemployment and workers’ compensation costs for businesses, will especially benefit upstate.

His upstate focus this year includes new agricultural marketing efforts – an initial one will center on beer, wine and yogurt industries – and duty-free stores across New York to promote agriculture products grown and made in the state.

The governor also is banking on casino development to help upstate. Lawmakers are poised again this year to consider second passage of a constitutional amendment – which would then go to voters this fall – permitting up to seven new Las Vegas-style casinos in New York.

Wednesday, Cuomo proposed a “first phase” that would limit the first three casinos to upstate. He did not say where they could go, but the proposal clearly protects two major track-based casinos in Queens and Westchester County.

“I believe casinos in upstate New York could be a great magnet to bring the New York City traffic up,” Cuomo said as he defended the controversial effort to dramatically expand gambling in New York. The state, he said, is already home to more than a dozen racetrack-based and Native American casinos, as well as 39 gambling facilities in border states and provinces.

Trying to get support for the plan, Cuomo proposed that 90 percent of casino proceeds – whether from an upfront franchise fee or through revenue-sharing money from slot machines – go to help fund state aid for public schools. The remaining 10 percent would go to property tax relief, though no details were offered.

Cuomo administration officials say the governor’s more liberal agenda is nothing that he didn’t promote during his 2010 campaign; now, they say, there is a greater opportunity for passage in a Senate that is run by a coalition of Republicans and several breakaway Democrats.

The nearly two-hour, highly choreographed event, with an accompanying 312-page booklet, was not all about liberal politics. The governor pushed new job-creation efforts, targeted tax breaks for certain kinds of companies and a $1.3 billion cut in unemployment and workers’ compensation costs for businesses – though he did not say how he would pay for them.

While the invited guests that filled a chilly Empire State Plaza Convention Center were mostly Cuomo allies, the hallways were filled with hundreds of protesters who came to Albany to demonstrate against his possible embrace of hydraulic fracturing, or “fracking,” of natural gas. The governor has signaled some interest in the controversial drilling practice.

The governor’s proposals include:

• Longer school years or school days to improve educational performance of students, though it is uncertain how much that will cost the state in what Cuomo said would be a voluntary program.

• New ways of funding community colleges to encourage better cooperation between schools and employers to help with job creation.

• A hike in the minimum wage from $7.25 per hour to $8.75 per hour.

• A new competition for 10 higher education/private sector high-tech incubation clusters, backed by tax-free incentives.

Other proposals include a dramatic increase in the number of electric car-charging facilities and a new upstate marketing effort. Cuomo also wants to create a $1 billion housing program and require public disclosure of all campaign contributions of more than $500 within a 48-hour period, instead of what is now as long as six months before those donations are revealed by campaigns. He also wants to permit New York to have early voting periods instead of a single Election Day.

The governor’s speech put a heavy emphasis on rebuilding efforts following Superstorm Sandy, and he is proposing a new “civilian emergency response corps” to help with future natural disasters across the state.

Exactly how Cuomo will pay for all the funding he is proposing – from a $1 billion “green bank” to help push the growth of environmentally “clean” companies to $50 million for a venture capital fund to help startups – is uncertain. It won’t be revealed until he proposes his 2013 budget in two weeks. The state already faces at least a $1 billion deficit in the coming fiscal year that starts April 1.

The speech recognized some of the fiscal realities the state faces. His plan to extend the school year or school day, which could carry enormous costs in teacher and administrative salaries, is limited; he wants a competitive grant program for only those school districts that extend the amount of learning time in a year by 25 percent.

Building on a teacher-evaluation system that is being phased in this year across New York, Cuomo also proposed a “bar exam” type of test for all new teachers seeking to work in the state’s public schools. He also would give $15,000 stipends to top teachers selected to instruct other teachers on classroom performance. He also proposed full-day prekindergarten classes in the state’s poorest districts – another expensive but popular idea among Democrats in the Assembly.

If there were any doubts that Cuomo’s third year in office will represent a shift to the political left, the governor ended them in his speech. Besides relaxing marijuana-possession laws, Cuomo proposed a number of what he called “progressive’’ plans, including mandatory recording of all criminal interrogations and the building of more than 14,000 housing units for low-income people.

On gun control, an idea pushed for years by Assembly Democrats but Cuomo began pressing after the mass shooting that killed 20 first-graders and six educators at a Connecticut school, the governor would eliminate large-capacity magazines in guns as a way to ban assault weapons, and to require background checks for gun sales between private parties and not just through gun shop or gun show sales.

He also wants longer prison sentences for crimes committed with guns or for incidents involving guns on school grounds. And he would require guns to be confiscated from individuals deemed by mental health professionals to be a danger to themselves or to others.

“No one hunts with an assault rifle,” said Cuomo, who owns a Remington shotgun.

The governor called his ideas “the most ambitious” agenda since he took office in 2011. Some ideas were new, some borrowed, and some renamed, such as providing certain tax breaks for “hot spot” areas of the state that was tried with the Empire Zone program. Besides the left-leaning rhetoric and proposals, it was reminiscent of his father’s annual speeches between 1983 and 1994 that were famous for their “kitchen sink” list of sometimes hundreds of proposals – making it difficult to discern the top priorities.

But the governor said the highly stacked list of ideas comes at a time when the state is trying to deal with many challenges – from a hurting upstate economy to the impact of Sandy.

“It’s more of a function of the needs of the time,” Cuomo said, adding, “We have daunting challenges.”