Flanked by law enforcement officials as well as the parents of children killed by people in the country illegally, Trump said, "Our immigration system is stretched beyond the breaking point" and called the congressional action "dangerous" and "reckless".
"As president, the protection of the nation is my highest duty", Mr Trump said on Friday.
We will add video when it becomes available.
US President Donald Trump issued the first veto of his presidency today (NZ time) to secure federal money for a border wall he promised as a candidate and considers a crucial priority for re-election, capping a week of confrontation with both political parties.
Twelve of Trump's fellow Republicans joined Democrats to pass the measure to end the emergency declaration.
The Republican senators who rebuked Trump were unwavering in their justification, saying Thursday they viewed the unilateral move as unconstitutional and creating a risky precedent for future presidents.
Trump made the construction of a wall along the nearly 2,000-mile-long US-Mexico border a cornerstone of his 2016 presidential campaign, saying Mexico would pay for it.
The emergency declaration is being challenged in court as an unconstitutional usurpation of Congress' power of the purse.
Mr Trump had declared the emergency in February after Congress refused his requests for $5.7bn (£4.4bn) to construct a border wall - a campaign promise.
Declaring a national emergency allows Trump to steer an extra $3.6 billion to the wall. "Think of that", he said.
On Friday, Barr also said the president's emergency order was "clearly authorized under the law". "That shift has placed a substantial strain on border-security resources".
While Congress is unlikely to muster the votes to override the veto, the rebuke from some members of his own party left Trump politically wounded, at least temporarily, as immigration and his planned wall along the USA southern border become a flashpoint again in the 2020 presidential campaign.
He also noted that despite record numbers of apprehensions at the border, there was not enough space to detain them all.