Amber Rudd appeared to hit out at Donald Trump after the US president claimed on Twitter that the Parsons Green bomber was known to police before the explosion.
The Home Secretary was referring to a tweet Mr Trump posted on Friday in the aftermath of the bombing, which injured 30 people.
The president wrote: 'Another attack in London by a loser terrorist. These are sick and demented people who were in the sights of Scotland Yard. Must be proactive!'
Speaking on The Andrew Marr Show this morning, Ms Rudd said Mr Trump’s controversial tweet was ‘pure speculation’ and not based on specific UK intelligence passed to Washington.
Refusing to comment: Home Secretary Amber Rudd won't say if police were already aware of the 18-year-old suspect
Trump tweeted: 'Another attack in London by a loser terrorist.These are sick and demented people who were in the sights of Scotland Yard. Must be proactive!'
He later walked back on his controversial comments, tweeting: 'Our hearts and prayers go out to the people of London, who suffered a vicious terrorist attack'
She said: ‘It is never helpful to have speculation about an on-going operation. I would include the President in that comment.’
When asked if she would tell the president to stop tweeting, she replied: ‘I don’t think I would be the first person to say that, would I?’
Ms Rudd's words come after it had emerged a second man, aged 21, had been apprehended by police in London in connection with the attack.
It follows the arrest of an 18-year-old man in Dover yesterday morning.
Yesterday the Home Secretary refused to say whether counter terror officials had had information on one of the attackers before the bombing.
When asked during an interview if it was concerning the suspect might have been already known to Scotland Yard, Mrs Rudd said: 'It's much too early to say that, we have one arrest and we have an going operation.'
But then she added: 'When we have more information, we will be sharing it.'
Mr Trump's tweet also angered the Prime Minister who said: 'I never think it's helpful for anybody to speculate on what is an ongoing investigation.'
She later challenged the president in person when he called her to discuss the case.
Yesterday Mrs Rudd described the arrest of the 18-year-old man as 'very significant' but would not respond to journalists questions about if Scotland Yard held information about him beforehand.
She said: 'The operation is ongoing.'
Investigators - who it is understood are linking the attack to Islamist extremism - are continuing their probe and the threat level remains at critical, which means a further attack is feared to be imminent.
The country's top counter-terrorism officer indicated that a potential network of plotters could have been involved.
A Scotland Yard spokesman criticised Mr Trump, saying: 'The comments are unhelpful and pure speculation. If anyone has got any evidence or information, please contact the anti-terrorism hotline.'
Security Minister Ben Wallace said yesterday morning that although it was 'not helpful to have a running commentary on a live investigation' he said about Trump's later tweets: 'I saw his follow-up statements. I think his sentiment was that the international community stands together in facing this threat.
'I think we can take that as being a good thing.'
Met terror chief Mark Rowley updated the media on the investigation this morning (pictured) but has not given any details of any man hunt
Keith Simpson, a Tory member of the Intelligence and Security Committee ahead of the election, last night told MailOnline Mr Trump's tweets would alarm some in Britain who could fear the security services knew of the plot and let it go ahead.
He said: 'Frankly, I don't know if that's the case.
'There will now be some interesting conversations going on between senior people in the Cabinet Office and the Trump Administration.
'He's done this kind of thing before. I think Theresa May has come as near as possible to say don't be so stupid.
'This is part and parcel of the way he deals with politics.'
U.S. National Security Advisor H.R. McMaster (right) told reporters at the White House on Friday that Trump wasn't speaking about any particular terror suspect when he claimed Scotland Yard had already had Friday's Tube bomber on its radar
President Donald Trump has claimed Scotland Yard knew ahead of time about a bomber or bombers who set off a crude incendiary bomb Friday morning on London's 'Tube' subway
Mrs May's former chief-of-staff Nick Timothy commented on Twitter, saying: 'True or not – and I'm sure he doesn't know – this is so unhelpful from leader of our ally and intelligence partner.'
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Images of Barcelons suspects Moussa Oukabir and brother Drissa emerged within a few hours of the Las Ramblas attack
More than seven hours after the terror attack in Parsons Green, police in London are still refusing to confirm whether they have a suspect.
The approach taken contrasts sharply with the response to the last major terror attack in Europe, Barcelona in August.
Just over an hour after the attack took place, Spanish police tweeted the public to say they were searching for the attacker and to avoid the area.
Then, within three hours after the attack, a photo of a suspect, Driss Oukabir, was released and circulated online.
The release of the image caused Oukabir to come forward to his local police and tell officers his documents had been stolen.
This was again revealed to the media as Oukabir's younger brother Moussa became the prime suspect.
Mr Trump appeared unconcerned about his diplomatic slip. Asked about the terror attack by reporters outside the White House, he said: 'It's a terrible thing.
'It just keeps going and going, and we have to be very smart, we have to be very, very tough. Perhaps we are not nearly tough enough. It's just an absolutely terrible thing. In fact, I'm going to call the Prime Minister right now.
'We have to be tougher and we have to be smarter.' He told reporters that he had been briefed on the explosion, but did not provide further details.
His national security adviser HR McMaster suggested later that Mr Trump was speaking generally.
Noting that law enforcement agencies have been working to combat terrorism for years, Mr McMaster said: 'I think if there was a terrorist attack here, God forbid, that we would say that they were in the sights of the FBI.'
He added: 'I think he means generally that this kind of activity is what we are trying to prevent.'
The controversy threatened to reopen the row between the UK and the US over the leaking of sensitive police information that led to the temporary suspension of security co-operation in the wake of the Manchester bombing.
Labour MP Stephen Doughty, a member of the home affairs select committee, said last night Mr Trump's intervention 'has the potential to not only undermine a vital relationship, but also to prejudice investigations into this and other incidents'.
Liberal Democrat home affairs spokesman Sir Ed Davey said: 'It is insulting to the victims of this attack that Donald Trump is already using it to try and further his divisive political agenda. Once again, Trump has shown he is not fit for the office of US President.'
London Mayor Sadiq Khan, who clashed with Mr Trump over his response to the London Bridge terror attack, would not be drawn on the president's comments. 'I've simply been too busy to look at my Twitter,' he said. 'My priority is making sure that we do what we can to keep Londoners safe.'
Trump added: 'Loser terrorists must be dealt with in a much tougher manner. The internet is their main recruitment tool which we must cut off & use better!'
Theresa May's former adviser Nick Timothy reacted to Trump's intervention by saying the president 'doesn't know' anything: 'This is so unhelpful from leader of our ally and intelligence partner'
Metropolitan Police officers were continued detailed searches and investigations at the scene of the bombing yesterday (pictured)
Police in and around London are hunting for the 'bucket bomber' who tried blow up a rush hour Tube train amid claims that he is armed and may have left other devices
The crude device could have killed dozens but failed to properly detonate and sent a 'wall of fire' through a subway car, injuring at least 22 people including a ten-year-old boy