The spokesman said May had spoken with US President Donald Trump, French President Emmanuel Macron, Italian Prime Minister Paolo Gentiloni and Australian Prime Minister Malcolm Turnbull and would likely have calls with other world leaders.

"The prime minister and the president agreed the international community needs to work together to tackle the ideology behind terrorist attacks. The president offered the United States' full support and cooperation," the spokesman told reporters of May's call with Trump.

May also visited the police headquarters and a children's hospital in Manchester on Tuesday, he said.