His re-election campaign also sought to raise money on the issue, sending a message to supporters in Trump's name that read, "I look forward to VETOING the Dem inspired OPEN BORDERS & Pro-Crime resolution!".
This is the first veto of Mr Trump's presidency.
Most Republicans who defected did so as a protest vote over the president's methods and their fear about the precedent of executive overreach rather than the underlying debate over whether a border wall is necessary.
Trump expressed pride in the Republicans who did not vote to support the resolution and said later that he had sympathy for those who defied him, adding they did what they had to do.
Trump has said he wants a wall to prevent immigrants from crossing into the United States, describing the situation as a national emergency.
Sen. Thom Tillis, R-N.C., had said he would oppose the declaration but reversed course on the Senate floor, saying that he was "sympathetic" to Trump's push to deal with the crisis at the border.
The emergency declaration came after Trump failed to win an appropriation for a border wall in a continuing resolution to fund the government last fall.
On Thursday, Trump tweeted "VETO!", following the Senate vote. He explained the legality of Donald Trump's countermeasure.
Declaring a national emergency allows Trump to steer an extra $3.6 billion to the wall. "That shift has placed a substantial strain on border-security resources".
The bill had passed the House in February with thirteen congressional Republicans crossing the aisle to join Democrats. The dozen senators who went against the White House were Susan Collins of Maine, Lisa Murkowski of Alaska, Roy Blunt of Missouri, Lamar Alexander of Tennessee, Pat Toomey of Pennsylvania, Rand Paul of Kentucky, Rob Portman of Ohio, Marco Rubio of Florida, Jerry Moran of Kansas, Roger Wicker of MS and Mitt Romney and Mike Lee, both of Utah.
Had Trump not taken action in a timely manner, the decisive votes would have overturned all the effort he put into securing funding for the Wall's construction.
Barr also made remarks and said President Trump's emergency declaration on the issue is "firmly grounded" in the law.
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