The dispute over wall funding - with Mr Trump demanding $5.7 billion just for this year to help build it - led to a stalemate in Congress over funding for parts of the government. Critics say the security risks are overblown and his administration is at least partly to blame for the humanitarian situation.
Trump repeated his call for a wall on the border, calling it "absolutely critical to border security".
Mr Trump's comments came at the start of the third week of a partial government shutdown that has left hundreds of thousands of federal workers idled or without paychecks. "The president has no authority to usurp Congress's power of the purse", House Judiciary Committee Chairman Jerrold Nadler, a Democrat from NY, said during a visit to the border on Monday.
He said he could relate to the workers who would have trouble paying bills because of the shutdown but threatened, again, to declare a national emergency as an alternative way to build the wall. But he made no mention of such a declaration in the Wednesday address from the White House.
Democrats have repeatedly slammed the proposed wall but have remained vague about counter-proposals that would curb illegal immigration.More news: Dick Cheney's daughter slams Christian Bale's 'Satan' comment — Golden Globes
Experts say if the shutdown persists, Canadians entering the US will see an escalating impact at the northern border, where Customs and Border Protection officials are working without pay because their jobs are considered an essential service. The Mexican government has refused to provide such funds.
"At the request of Democrats, it will be a steel barrier rather than a concrete wall". There were almost 400,000 apprehensions at the border in the 2018 fiscal year, well down from the early 2000s when arrests regularly topped one million annually.
"The border wall would pay for itself".
Two days after Trump's speech, he plans to visit the southern border, the White House announced earlier in the week.
The fact-checking nonprofit PolitiFact, run by the Poynter Institute, said on Twitter that it will live fact-check the president's address Tuesday night. Recent reports and studies show that illegal border crossings have actually dropped and a majority of Americans are against the wall, but such studies go against the Trump narrative of a grave crisis at the Southern border that required a massive wall across 2000 miles.More news: Mike LaFleur expected to stay with 49ers after Packers hire brother
"The fact is: President Trump must stop holding the American people hostage, must stop manufacturing a crisis, and must reopen the government".
The big question was whether Trump would use the occasion to declare a national emergency at the border, giving himself considerable new powers and sidestepping Congress's control of the purse strings.
During the campaigning he pledged Mexico would pay for the wall, but since taking office he has been unable to achieve this, and is now attempting to use USA taxpayer funds to the tune of US$5.7 billion (NZ$8.5b).
The shutdown, now into its 18th day, follows disagreement between the new Democrat-controlled House and the White House over budgeting several government departments whose funding has lapsed.More news: National Football League world reacts to Cody Parkey's missed field goal