Lower courts have blocked the policy, citing various reasons including statements Mr Trump made during the 2016 presidential election campaign.

The legal fight pits the president's authority over immigration against what lower courts have said is a policy that purported to be about national security but was intended to target Muslims.

Mr Trump later called Theresa May, the Prime Minister, to offer his condolences.

The White House said the president "praised the heroic response of police and other first responders and offered the full support of the United States government in investigating and bringing those responsible for these heinous acts to justice".