US President Barack Obama didn't mention any presidential candidates during his final State of the Union address on Tuesday, but Donald Trump and his fiery rhetoric against Muslims and immigrants were clearly on his mind.

In remarks to Congress, Obama sought to lay out his vision for the future regardless of who is elected the next president, but it's clear he would like his vision to be carried on by a successor from his centre-left Democratic Party.

Obama dismissed his Republican opponents as "peddling fiction" with claims of US economic and international decline, and called for the rejection of "any politics that targets people because of race or religion."

Trump, the Republican frontrunner, entered the election contest by denigrating Mexican immigrants and vowing to build a wall on the southern border. He called for banning the entry of all Muslims into the United States after a terrorist attack in California last month.

Obama denounced such rhetoric as diminishing the US on the world stage and betraying the universal values on which the country was founded.

"When politicians insult Muslims ... that doesn't make us safer," he said. "That's not telling it like it is. It's just wrong."

Trump seems to have only gained followers with his unfiltered comments that run against traditional political wisdom.

A CBS News/New York Times poll released Tuesday shows Trump leading nearest rival Ted Cruz by 16 percentage points nationally. Trump garners 36 per cent to Cruz's 19 and Marco Rubio's 12 per cent.

Much of Trump's support comes from outside traditional Republican circles. The party establishment has expressed concern that he could damage the party, while also seeking to prevent him from staging a third-party bid that could scuttle another Republican candidate.

South Carolina Governor Nikki Haley, who was tapped by the party to deliver the Republican response to Obama, took her own jab at Trump.

"During anxious times, it can be tempting to follow the siren call of the angriest voices. We must resist that temptation," said Haley, the daughter of Indian immigrants.

"No one who is willing to work hard, abide by our laws, and love our traditions should ever feel unwelcome in this country."

For his part, Trump provided very little commentary on Obama's speech to Congress, but declared on Twitter: "The #SOTU speech is really boring, slow, lethargic - very hard to watch!"

Cruz said Obama "continues to be in denial of reality," knocking the president's handling of the economy, the fight against Islamic State and his partisan rhetoric.

"He lectures us on civility yet has been one of the most divisive presidents in American history," Cruz said.

Obama acknowledged one of his few regrets from his nearly two terms in office is "that the rancor and suspicion between the parties has gotten worse instead of better."

Rubio and Senator Bernie Sanders, a Democratic presidential candidate, were the only candidates in the audience as other lawmakers in the presidential field remained on the campaign trail.

Sanders and Democratic frontrunner Hillary Rodham Clinton praised Obama's remarks.

Clinton, who as Obama's first secretary of state is the candidate most closely associated with his legacy, declared on her Twitter account: "Seven years of progress. We need to build on it - not go backwards."

Despite his serious words on political rhetoric, Obama opened with a joke about the campaign that will soon pick his successor.

"I know some of you are antsy to get back to Iowa," where the first caucus will be in just under three weeks, he joked. "I've been there. I'll be shaking hands afterward if you want some tips."

The first in a series of intra-party contests to determine party nominees will be held in the central state of Iowa on February 1, followed by New Hampshire on February 9.

The Republican and Democratic nominees will face off in the presidential election on November 8.

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