"Congress has rejected the president's declaration, and now the courts will be the ultimate arbiter of its legality".
Republican senators who bucked the president said they did so to preserve congressional control over the government's purse strings.
This is the first veto of Mr Trump's presidency.
The Republican-controlled U.S. Senate voted to end his border emergency declaration, with 12 of Trump's fellow Republicans joining Democrats.
Shortly after the veto was official, House Speaker Nancy Pelosi announced that the vote to potentially override the veto would occur on March 26, saying "House Republicans will have to choose between their partisan hypocrisy and their sacred oath to support and defend the Constitution". "This is not about the president or border security, in fact I support border security, I support a barrier".More news: Tucker Carlson's Refusal to Apologize Is the 'Fox News Brand'
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The emergency declaration is being challenged in court as an unconstitutional usurpation of Congress' power of the purse. Almost all have noted that future Democratic presidents would exploit Trump's action and declare their own national emergencies to fulfill campaign promises.
Trump is seeking a total of $8 billion for his wall: $1.375 billion approved by Congress, $600 million from the Treasury Department's drug forfeiture fund, $2.5 billion from the Defense Department's drug interdiction efforts and roughly $3.5 billion from Department of Defense military construction. The 12 GOP senators, including the party's 2012 presidential nominee, Mitt Romney of Utah, joined the dissent over the emergency declaration order that would enable the president to seize for the wall billions of dollars Congress meant to be spent elsewhere.
"I think the basic premise of Mike [Lee's] bill is correct", Republican Senator Jerry Moran said Thursday.
Barr also made remarks and said President Trump's emergency declaration on the issue is "firmly grounded" in the law. "To me, border security is national security".
The wall was a signature campaign issue for Trump, but he was never able to deliver on his promise to make Mexico pay for it, and the issue languished during his first two years in office.