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WASHINGTON — President Trump challenged Democrats on Tuesday night to join him in overhauling immigration policies and in rebuilding the nation’s infrastructure in his first State of the Union address.

Speaking to a joint session of Congress, Mr. Trump hailed what he called the “extraordinary success” of his administration’s first year, and largely steered clear of the nationalist rhetoric, political attacks and confrontational tone that have been his calling cards both as a candidate and as a commander in chief.

“Tonight, I call upon all of us to set aside our differences, to seek out common ground and to summon the unity we need to deliver for the people,” Mr. Trump said to raucous applause from many Republicans, as Democratic leaders who have bitterly criticized his policies and messaging sat stone-faced in their seats.

“This, in fact, is our new American moment,” Mr. Trump said. “There has never been a better time to start living the American dream.”

In an address remarkably devoid of new policies, Mr. Trump instead recited what he described as his greatest accomplishments and laid out an improbable agenda for a Congress facing midterm elections in the fall.

He said he would bring Republicans and Democrats together around a $1.5 trillion infrastructure plan to “give us the safe, fast, reliable and modern infrastructure our economy needs and our people deserve.” And he dared Democrats to reject what he called a “down-the-middle compromise” on immigration where “nobody gets everything they want, but where our country gets the critical reforms it needs.”

“For over 30 years, Washington has tried and failed to solve this problem,” Mr. Trump declared. “This Congress can be the one that finally makes it happen.”

The president avoided the most controversial elements of his presidency, saying nothing about the investigations into Russian interference in the 2016 election and whether Mr. Trump or his associates helped the effort or obstructed justice.

The president did not acknowledge the “Me Too” movement of women speaking out against sexual harassment and assault. He also left out some standard grievances. He did not renew his threats to crack down on so-called sanctuary cities that decline to work with federal immigration authorities, nor did he devote much time to promising to rip up trade agreements.

Democrats in the chamber spent much of the speech refraining from applause, scowling at his boasts, and at one point hissing in disapproval at his proposal for restricting the number of family members immigrants can bring to the United States. As he took the dais at the Capitol, Mr. Trump had the weakest approval rating of any president of the modern era entering his second year in office, with 37 percent of Americans approving of his performance in the job.

But Mr. Trump stepped behind the lectern still popular with his most ardent supporters, who see him as an unpredictable and entertaining commander in chief who posts vitriol on Twitter against the advice of the White House staff, the Republican leadership and those closest to him.

Mr. Trump built his speech around the theme of heroes, using the stories of ordinary people who had overcome extraordinary challenges — a police officer who adopted the child of a heroin-addicted mother, an Army staff sergeant who won the Bronze Star while fighting in Syria, a North Korean defector who now rescues other defectors — to argue that “the state of our union is strong because our people are strong.”

Most presidents have made sure that there is a choreographed rollout of political messages and policy prescriptions before a State of the Union address. But Mr. Trump’s past week has been consumed by the revelationthat he sought last year to fire Robert S. Mueller III, the special counsel leading a Russia investigation, and by the abrupt departure of the F.B.I. deputy director, Andrew G. McCabe, whom the president had railed against as politically corrupt.

At the same time, Republicans are pushing to make public a classified memo that they say shows a politically driven effort by the F.B.I. and the Justice Department to malign Mr. Trump with manufactured allegations of links to Moscow. Democrats say the memo is a set of cherry-picked facts to distort the origins of the Russia investigation and undermine the inquiry. On his way out of the chamber, Mr. Trump could be heard reassuring a Republican congressman that he supports the release of the memo “100 percent.”

Presidents historically use the annual State of the Union address to tout the successes of their administrations. Mr. Trump went even further, using his time in the spotlight to describe what he views as his major successes during his first year in office: job growth, the confirmation of Neil M. Gorsuch to the Supreme Court, the rollback of regulations, a $1.5 trillion tax cut, the defeat of the Islamic State in Iraq and Syria and historic gains in the stock market.

“Just as I promised the American people from this podium 11 months ago, we enacted the biggest tax cuts and reform in American history,” Mr. Trump said.

Mr. Trump delivered his roughly 80-minute speech — the longest since President Bill Clinton in 2000 — almost verbatim from a teleprompter, staying uncharacteristically faithful to his prepared script as he paused for ovations, savoring an opportunity to promote his agenda and reaching for lofty statements about the strength of what he called “one American family.”

Yet similar rhetoric by Mr. Trump has not lasted long. When he addressed a joint session of Congress weeks after his inauguration last year, Mr. Trump called for an end to “trivial fights.” Days later, he was on Twitter charging that President Barack Obama had tapped his phones in Trump Tower.

Mr. Trump’s tone became markedly sharper as he turned to the issue of immigration, seeking to link crime and terrorism to the United States’ immigration policies. He highlighted the parents of young girls killed by immigrants who entered the country as “illegal, unaccompanied alien minors,” saying it was time for Congress to “finally close the deadly loopholes that have allowed MS-13 and other criminal gangs to break into our country.”

The president delivered his speech in the middle of an intense immigration debate in Congress about the fate of the so-called Dreamers, young people who were brought illegally to the United States as children. Mr. Trump has repeatedly expressed sympathy for the Dreamers and used the speech to reiterate his proposal to grant them legal status, including a path to citizenship, in exchange for stepped-up enforcement, the building of a wall on the southern border with Mexico and a reordering of immigration laws that gives priority to higher-skilled immigrants.

“It is time to reform these outdated immigration rules, and finally bring our immigration system into the 21st century,” Mr. Trump said.

The president, who shocked lawmakers this month at an Oval Office meeting by using a vulgar term to disparage African nations, went out of his way to present himself as tolerant and appreciative of the nation’s diverse people.

“So tonight I am extending an open hand to work with members of both parties, Democrats and Republicans, to protect our citizens, of every background, color, religion and creed,” he said.

But the proposal has drawn condemnation from Democrats who call it meanspirited and anti-immigration activists who see it as an unacceptable grant of amnesty.

Democrats used the occasion to send their own message to Mr. Trump on the matter: They invited Dreamers who were to lose their protections from deportation — as well as family members of people the Trump administration has detained and deported — to sit with them in the House chamber as the president spoke.

Mr. Trump provided little in the way of specifics on the infrastructure proposal, other than to say that it should tap into private-sector and state and local funds in addition to federal dollars for a national initiative to “reclaim our building heritage.” Although the idea has wide bipartisan appeal, the details have the potential to start regional battles among lawmakers and partisan fights over how to pay for it.

The president also promoted what he called his achievements around the world, caling for steep investments to make the American military “so strong and powerful” and hailing victories against the Islamic State, also known as ISIS, as a vindication of his pledge last year to extinguish the group “from the face of the earth.”

“One year later, I am proud to report that the coalition to defeat ISIS has liberated very close to 100 percent of the territory just recently held by these killers in Iraq and Syria,” Mr. Trump said.

Mr. Trump touted his decision to move the American Embassy in Israel to Jerusalem and he announced, as expected, that he has signed an executive order to keep operating the Guantánamo Bay prison — a symbolic act that effectively keeps the detention facility open for business.

He also called on Congress to make sure that foreign assistance dollars “only go to America’s friends.”

The president included a tough message to the North Korean government and a denunciation of Kim Jong-un as a leader who has brutalized his own people and must be made to relinquish his nuclear program.

Adding drama to moment, he paid tribute to previously unannounced guests who wept in the gallery: the parents of Otto Warmbier, the University of Virginia student who died after being detained for 17 months in North Korea. And he hailed the escape of Ji Seong-ho, a North Korean defector who lost his leg before his harrowing journey.

“Today he has a new leg, but Seong-ho, I understand you still keep those crutches,” Mr. Trump said as the young man triumphantly waved the crutches over his head.