United States President Donald Trump has issued the first veto of his presidency, overruling the US Congress to protect his emergency declaration for border wall funding.

Flanked by law enforcement officials and by the parents of children who were killed by people in the country without documentation, Trump on Friday maintained that he was not through fighting for his signature campaign promise, which stands largely unfulfilled 18 months before voters decide whether to grant him another term.

"Congress has the freedom to pass this resolution," Trump said, "and I have the duty to veto it."

A dozen defecting Republicans joined Senate Democrats in approving the joint resolution on Thursday, which capped a week of confrontation with the White House as both parties in Congress strained to exert their power in new ways.

On Thursday, Trump tweeted "VETO!", following the Senate vote.

It is unlikely that Congress will have the two-thirds majority required to override Trump's veto, though House Democrats have suggested they would try nonetheless.

After Trump signed the expected veto, US House Speaker Nancy Pelosi said the body planned to vote for a veto on March 26 and potentially override Trump's move.