London's Mayor has slapped down Donald Trump's "ill-informed" tweeting after the London Bridge terror attack, accusing the US President of deliberately taking a statement about increased police presence out of context.

In a series of tweets after the attack, Mr Trump criticised London's Mayor Sadiq Khan and argued on Twitter that leaders need to "stop being politically correct" and focus on "security for our people".

Seven people were killed and about 50 others injured when a van mowed down pedestrians on London Bridge before three attackers stabbed pub-goers at the nearby Borough Market.

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The US President challenged Mr Khan for saying there was "no reason to be alarmed" about the increased number of police on the streets in the wake of the attack.

But the Mayor's spokesperson said Mr Trump's tweet "deliberately takes out of context" Mr Khan's remarks urging Londoners not to be alarmed when they see armed officers on the streets.

The Mayor's spokesperson said he was too busy to respond to Mr Trump's "ill-informed" tweeting.

Earlier, Mr Khan described a more visible police presence as "one of things the police and all of us need to do to make sure we are as safe as we possibly can be".

"My message to Londoners and visitors to our great city is to be calm and vigilant today," he said in a TV interview.

"You will see an increased police presence today, including armed officers and uniformed officers. There is no reason to be alarmed by this."

The US President sent a trio of tweets in response:

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Shortly after the third tweet directed at London's Mayor, Mr Trump left the White House and was driven to his private golf club in Northern Virginia.

Despite requests, aides provided no information on his activities during several hours at the club.

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Promoting travel ban as London attack unfolds

Before criticising Mr Khan, Mr Trump also pushed his stalled travel ban, took on gun control supporters and pledged that the United States will help London and the United Kingdom.

First, he retweeted a Drudge Report item about the attack, then provided his own message about the travel ban.

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A few minutes later Mr Trump tweeted a message of support for Londoners:

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Earlier this week, the Trump administration asked the Supreme Court to immediately reinstate its ban on travellers from six mostly Muslim countries and refugees from anywhere in the world.

The administration argues that the US will be safer if the policy is put in place.

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

ABC/AP