The divide between the US administration and congressional Democrats on funding a border wall was laid bare before a national audience who followed President Donald Trump's first televised Oval Office address and a rebuttal from two congressional leaders on Tuesday night.

The speech was made at a time when the partial government shutdown headed into a third week over the budget standoff between the president and Congress.

Analysts said the impasse is going to linger, though both sides have agreed to continue talking.

In his nine-minute national address, Trump laid out his case for the wall on the southern border with Mexico, which he said is laden with "a growing humanitarian and security crisis".

"This barrier is absolutely critical to border security," Trump said, adding that doing it or not is "a choice between right and wrong, between justice and injustice".

"There is a growing humanitarian and security crisis at our southern border," he said. "Every day customs and border patrol agents encounter thousands of illegal immigrants trying to enter our country.

"We are out of space to hold them and we have no way to promptly return them back home to their country," Trump said. "America proudly welcomes millions of lawful immigrants who enrich our society and contribute to our nation. But all Americans are hurt by uncontrolled illegal migration."

Trump stopped short of calling for a state of emergency, instead appealing to the need to slash the cost of the illegal drug trade, which he put at $500 billion a year, "vastly more than the $5.7 billion we have requested from Congress".

Minutes after Trump's speech, House Speaker Nancy Pelosi said the president has "chosen fear" in making the case to the American people for the border wall, and Democrats "want to start with the facts".

"The fact is President Trump has chosen to hold hostage critical services for the health, safety and well-being of the American people and withhold the paychecks of 800,000 innocent workers across the nation – many of them veterans," she said. "He promised to keep government shutdown for 'months or years' – no matter whom it hurts. That's just plain wrong."

Senate Democratic leader Chuck Schumer said Democrats and Republicans agree on the need to secure borders, but he said "the symbol of America should be the Statue of Liberty, not a 30-foot wall".

He urged the president to "reopen the government and we can work to resolve our differences over border security. But end this shutdown now."

Cal Jillson, a political scientist and historian at Southern Methodist University, said he believed President Trump's national address on the nation's most prestigious podium was "not compelling".

"More effective was Senator Chuck Schumer, the Democratic leader of the Senate, who argued that the symbol of the nation should be the Statue of Liberty not a 30-foot wall."

Jillson also said Wednesday's meeting between Trump and Republican lawmakers at the Capitol is unlikely to produce much movement.

"President Trump is slowly bleeding support among moderate Republicans in Congress. At some point, he may still declare a national emergency, claim to his supporters that he had done everything he could and open the government," Jillson said. "The courts would likely question, even challenge, the president's claim to emergency powers."

William C. Banks, a law professor of Syracuse University College of Law, also said Trump is likely to rely on authority provided by Congress in the National Emergencies Act (1976) to declare a national emergency at the southern border, then rely on military construction statutes that may enable him to spend for wall construction without a new appropriation for that purpose.

"The president's legal arguments are contentious and may be wrong, based on the above authorities. Congress could stop him by passing a law saying no funding for a wall, or they could limit the funds available," he told China Daily in an email.