"Congress has the freedom to pass this resolution, and I have the duty to veto it."
The president called the resolution "dangerous", "reckless" and a "vote against reality", The New York Times reported.
Trump was flanked by Vice President Mike Pence, Attorney General William P. Barr and Homeland Security Secretary Kirstjen Nielsen.
The veto, which was expected, will send the legislation back to Congress, which almost certainly does not have enough votes for an override, which means Trump's declaration will remain in effect.
Rebuffed by Congress in his demands for billions for the wall, Trump had declared a national emergency at the Mexican border last month, a move that would allow the President to circumvent the will of lawmakers and spend billions on border barriers, said The Washington post.
Congress backed a resolution of disapproval, with the Senate voting 59-to-41 on Thursday for the measure.
Twelve "rebel" Republicans defied Trump and joined the Democrats on the legislation.
Democrats were quick to condemn the President's action on Friday.
"It is no surprise that the president holds the rule of law and our Constitution in minimal regard," Senator Chuck Schumer of New York said in a statement.
"There is no emergency; Congress has refused to fund his wall multiple times; Mexico won't pay for it; and a bipartisan majority in both chambers just voted to terminate his fake emergency."
House Speaker Nancy Pelosi said: "The House and Senate resoundingly rejected the President's lawless power grab, yet the President has chosen to continue to defy the Constitution, the Congress and the will of the American people."
Trump has long insisted that there was a security and humanitarian crisis at the border with Mexico, an assertion that was undercut by the President himself when he acknowledged that he could have waited to issue a declaration.
But on Friday, he offered a flurry of statistics to support his contention, though many were unverified, The New York Times said.
Even if Congress fails to override the veto, the emergency declaration is already drawing court challenges.
Last month, a coalition of 20 states, including California and New York, sued over Trump's use of emergency powers, arguing that the President does not have the authority to divert funds for building a wall along the Mexican border because it is Congress that controls the spending.