Speaking to the UK's Channel 4 News, London Mayor Sadiq Khan reiterated that he thought a planned state visit to the UK for Trump should be called off.
"I don't think we should roll out the red carpet to the President of the USA in the circumstances where his policies go against everything we stand for," Khan said.
"When you have a special relationship it is no different from when you have got a close mate. You stand with them in times of adversity, but you call them out when they are wrong. And there are many things about which Donald Trump is wrong."
He said his position on the planned state visit had remained consistent.
In January of this year, Khan insisted Trump's state visit to Britain be canceled after the US President attempted to impose a travel ban on Muslim nations -- a policy that he labeled "cruel and shameful."
The British politician was largely dismissive of two tweets sent by Trump in the wake of the attacks, which misconstrued a statement from Khan.
In the immediate aftermath of the attack, Khan said there was "no cause for alarm" when referring to a visible increase in police activity on the streets of London.
Trump appeared to misconstrue the statement on Sunday when he tweeted: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is "no reason to be alarmed!"
Trump renewed his criticism of Khan on Monday, a day after attacking his handling of the weekend's terror attack
in the city.
Trump said: "Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his 'no reason to be alarmed' statement. (Mainstream media) is working hard to sell it!"
Following a vigil held near the city's famous Tower Bridge, Khan said that as he deals with the fallout from the latest attack on the British capital, he hasn't "got the time to respond to tweets from Donald Trump."
PM backs Mayor
Prime Minister Theresa May came to Khan's defense, saying he was doing a "good job" and that they were working together closely in the wake of the weekend attack.
"I think Sadiq Khan is doing a good job and it's wrong to say anything else -- he's doing a good job," May told reporters after a general election campaign speech.
May declined to directly criticize Trump for his tweet, which has prompted a fierce backlash in Britain.
Asked what it would take for her to publicly criticize the US President, May suggested that she "was not afraid" to speak out when Trump "gets things wrong."
"I've been very clear, I've been very happy to say when I think President Trump is wrong -- to have taken America out of the climate change agreement, the Paris agreement," May said. "So I'm not afraid to say when I think President Trump is getting things wrong."'
After Trump's first attack on Khan, the acting US ambassador to the UK, Lewis Lukens, notably singled out the London Mayor for praise.
"I commend the strong leadership of the @MayorofLondon as he leads the city forward after this heinous attack," read a tweet from the US' London embassy attributed to Lukens.