The standoff has resulted in a partial government shutdown since 22 December.
The unexpected length of the shutdown has raised the prospect that Trump would begin to lose support among Republicans anxious to reopen the government and doubtful of the White House strategy.
Mr Trump had spent days mulling declaring a state of emergency along the border that would have given him powers to bypass Congress, which has so far refused to fund the wall project, and draw funds from the military to build the border barrier.
At a private meeting with House Republicans, Vice President Mike Pence cited a C.S. Lewis quote calling courage a virtue, and he said Trump has no plans to retreat.
"And he just got up and said, 'Then we have nothing to discuss, ' and he just walked out".
"There is a crisis that the president and his administration have created, and it's a humanitarian crisis of the people at the southern border whom are seeking asylum".
This has led to a standoff, the partial shutdown of the US government, and what the president calls a "crisis" at the border.
"America's heart broke the day after Christmas, when a young police officer in California was savagely murdered in cold blood by an illegal alien, who just came across the border", Donald Trump said in his address. "... We have a crisis at the border... it is national security; it's a national emergency".
Democrats also argue that a mix of fencing, which already has been constructed in many parts of the border, and higher-tech tools would be cheaper and more effective in securing the border.
For now, Trump sees this as winning politics.
He addressed the nation as the shutdown stretched through its third week, with hundreds of thousands of federal workers going without pay.
Some Democrats have in the past been willing to negotiate some sort of wall funding in exchange for presidential backing of immigration changes that would allow people brought to the US illegally as children receive legal status.
Fox News also had more total viewers than broadcast network ABC, which averaged 5.8 million viewers during Trump's remarks and the response, which was delivered by House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer.
Trump will follow up his speech with a rare trip to the Mexico border on Thursday, but showed little enthusiasm for either the Oval Office speech or the border trip during an off-the-record lunch Tuesday with television anchors, The New York Times reported.
But critics say the security risks are overblown and his administration is at least partly to blame for the humanitarian situation.
Of course, the content of Trump's address-a clear, immigrationist restrictionist message-remained deeply divisive on an increasingly crucible issue in American life.
He claimed to have met "dozens of families whose loved ones were stolen by illegal immigration.I've held the hands of the weeping mothers". So sad. So bad.