WASHINGTON — President Barack Obama, seeking to put the prosperity and promise of the middle class at the heart of his second-term agenda, called on Congress on Tuesday night to raise the federal minimum wage to $9 an hour, saying that would lift millions out of poverty and energize the economy.

In a State of the Union address that fleshed out the populist themes of his inauguration speech last month, Obama declared it was “our generation’s task” to “reignite the true engine of America’s economic growth — a rising, thriving middle class.”

“A growing economy that creates good middle-class jobs — that must be our North Star,” he said. “Every day, we should ask ourselves three questions as a nation: How do we attract more jobs to our shores? How do we equip our people with the skills to do those jobs? And how do we make sure that hard work leads to a decent living?”

The increase in the minimum wage — from its current $7.25 an hour — was the most tangible of a raft of initiatives laid out by the president, from education to energy, which Obama said would accelerate the nation’s economic recovery by helping those in the broad middle class.

Raising the minimum wage, which the White House said would affect at least 15 million workers, also holds political appeal for the younger Americans, struggling workers and labor groups, all of which were important to Obama’s re-election victory.

Speaking to a divided Congress, with many Republicans still smarting from his electoral victory last November, Obama declared, “Together, we have cleared away the rubble of crisis, and say with renewed confidence that the state of our union is stronger.”

He urged lawmakers to act on immigration, climate change, the nation’s fiscal woes, and above all, gun violence, offering an emotional appeal that drew heavily on recent tragedies like the mass shooting in Newtown, Conn. If they do not move, he said, he will use his executive authority to enact his own measures.

Obama also spoke darkly of the consequences of a failure to reach a budget deal, which would set off automatic spending cuts on the military and other government programs.

“These sudden, harsh, arbitrary cuts would jeopardize our military readiness,” he said, describing them as a “really bad idea.”

Obama took the podium after a rousing welcome from lawmakers and other dignitaries. But millions of TV viewers, not to mention people glancing at their phones inside the chamber, were distracted by a manhunt unfolding across the country, where police in the San Bernardino Mountains of California were tracking Christopher J. Dorner, a suspect in the killing of several officers. News coverage concentrated on the search almost up to the point the president entered the chamber.

Republicans rejected Obama’s activism, saying it would inevitably translate into higher taxes and an overweening government role, strangling growth and deepening the nation’s fiscal hole.

But in selecting Sen. Marco Rubio, a Cuban-American from Florida, to deliver their party’s official rebuttal, Republicans implicitly acknowledged the damage they had suffered at the polls from their hard line stance on immigration. Rubio, one of the party’s rising stars, favors overhauling immigration laws.

In a speech dominated by domestic issues, Obama admonished North Korea a day after it tested a nuclear weapon, rattling its Pacific Rim neighbors. He warned the country’s reclusive government that it faced further isolation, swift retaliation, and a United States bent on improving its own missile defense systems.

But as new threats erupted, old threats, Obama said, were receding. He announced, for example, that 34,000 troops would return home from Afghanistan by this time next year. That withdrawal, representing half the current U.S. force, underlined his resolve to wind down the second war of his presidency as quickly as he did the one in Iraq.

Obama was not trying to match the lofty tone of his inauguration speech, but the address was clearly intended to be its workmanlike companion. In place of his ringing call for a more equitable society was a package of proposals — some requiring legislation; others merely an executive order — that constitute a blueprint for the remainder of his presidency.

Among the proposals was a $1 billion investment to create 15 institutes to develop new manufacturing technologies, building on the success of a pilot project in Youngstown, Ohio. He said he would use oil and gas royalties from federal lands to pay for research in clean energy technology that would wean cars and truck off oil. And he recycled a proposal to help homeowners refinance their mortgages at lower rates.

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Unmentioned this year was a special law enforcement unit he created last year to crack down on abusive lending. Critics say the unit, under the leadership of Attorney General Eric H. Holder Jr., was ineffective, though the administration said it led to hundreds of criminal indictments.

None of his proposals, Obama said, would add to the deficit, since they were consistent with the budget deal of 18 months ago. “It’s not a bigger government we need,” he said, “but a smarter government that sets priorities and invests in broad-based growth.”

Still, Obama signaled that the era of single-minded deficit-cutting should end. He noted that the recent agreements on taxes and spending reduced the deficit by $2.5 trillion, more than halfway toward the $4 trillion in reductions that economists say would put the nation’s finances on a sustainable course.

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The most impassioned parts of the speech echoed those that Obama delivered on the west front of the Capitol three weeks ago.

“It is our unfinished task to restore the basic bargain that built this country,” Obama said. “The idea that if you work hard and meet your responsibilities, you can get ahead, no matter where you come from, what you look like, or who you love.”

“It is our unfinished task to make sure that this government works on behalf of the many, and not just the few,” he said. “That it encourages free enterprise, rewards individual initiative, and opens the doors of opportunity to every child across this great nation of ours.”

Children loomed large at this State of the Union. Among the guests were survivors of the Newtown shooting and the parents of Hadiya Pendleton, the 15-year-old high school majorette whose shooting death in Chicago has become an emblem of the grim toll of gun violence. They were guests of the first lady, Michelle Obama.

Gesturing to Hadiya Pendleton’s parents, Obama said: “They deserve a vote. Gabby Giffords deserves a vote. The families of Newtown deserve a vote. The families of Aurora deserve a vote.”

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On climate change, Obama endorsed the cap-and-trade legislation once championed by Sen. John McCain, R-Ariz., and former Sen. Joseph I. Lieberman of Connecticut, but long stalled in Congress. Though the president said he would not hesitate to use executive orders to push his own measures to reduce carbon emissions, he did not give any details.

In another sign of the election’s lingering shadow, Obama was creating a bipartisan commission to investigate voting irregularities that led to long lines at polling sites in November. Studies indicate that these lines cost Democrats hundreds of thousands of votes. The commission will be led by the chief counsel of the Obama presidential campaign, Robert Bauer, and a legal adviser to Mitt Romney’s campaign, Ben Ginsberg.

On trade policy, the president said that the United States and the European Union were ready to begin negotiations on a comprehensive trade treaty. That came after a report submitted earlier in the day concluded that the gaps between the two sides were narrow enough to put a deal within reach.

Obama also revisited one of his signature initiatives: a pledge to reduce the size of the nation’s nuclear stockpiles in negotiations with Russia.