US President Donald Trump renewed his online criticism of London Mayor Sadiq Khan on Monday, calling his statements "pathetic" in the wake of Saturday's terrorist attack.

"Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his 'no reason to be alarmed' statement," Trump wrote on Twitter. He accused the media of "working hard to sell it!".

Trump had gone after Khan a day earlier for telling Londoners not to be alarmed, but faced criticism for taking the mayor's remarks out of context.

Khan's remarks about not being alarmed referred to the heightened police presence in the city, not with the threat of terrorism itself.

Seeking to reassure London residents and visitors, Khan had told BBC Radio on Sunday that "Londoners will see an increased police presence today and over the course of the next few days. There's no reason to be alarmed."

White House spokeswoman Sarah Sanders said Trump was stressing the importance of national security and maintained the president had not misrepresented what Khan had said.

"The point is there is a reason to be alarmed, we have constant attacks going on, not just there but around the globe and we have to start putting national security, global security at an all-time high," she said.

Following Trump's first barrage of tweets Sunday, the London mayor's press office said Khan had more important things to do than respond to the US president's "ill-informed tweet".

Theresa May, Britain's Conservative prime minister, said it was wrong to criticise Khan, who represents the opposition Labour party, praising him for his response to Saturday's attack and saying he is "doing a good job" as mayor.

"I think Sadiq Khan is doing a good job and it's wrong to say anything else," May told reporters Monday at an election campaign event when asked about Trump's attacks on Khan.

May declined to criticise Trump for his remarks, but she said she had disagreed with the US leader on issues such as climate change.

"I have been critical of Donald Trump before. I don't think he should have pulled out of the climate agreement," she said.

In London, Lew Lukens, the acting US ambassador, also contradicted Trump, praising Khan's leadership.

"I commend the strong leadership of the mayor of London as he leads the city forward after this heinous attack," Lukens said in a tweet late Sunday.

A YouGov survey last week found that Khan enjoys greater public trust to keep London secure than either May or her main rival, Labour leader Jeremy Corbyn.

YouGov found 51 percent of Londoners trusted Khan to "make the right decisions about keeping Britain safe from terrorism," with 30 percent saying they did not trust him.

May and Corbyn shared similar levels of trust and distrust, with 42 percent saying they trust May and 41 percent trusting Corbyn, while 46 percent said they don't trust the prime minister and 47 percent said the same about the Labour leader.

Trump and Khan have traded criticism since before the real estate mogul was elected US president.

Khan, who became the first Muslim mayor of a major Western capital city when he was elected in 2016, in October called Trump's campaign pledge to ban Muslims from entering the US "ignorant."

Khan said earlier this year Trump should be denied a state visit to Britain due to his "cruel and shameful" immigration policies.

The date of Trump's first visit to Britain as president has not yet been finalised. The invitation for an official state visit was extended to Trump by May after just a week in office.

- dpa