Khan and Trump publicly feuded following the June attacks after the US President misconstrued a statement from Khan saying there was "no cause for alarm" due to the visible police activity following the incident.
"These are sick and demented people who were in the sights of Scotland Yard".
In short remarks to reporters, Trump said he had been briefed on the explosion but did not elaborate on what he meant in his reference to Scotland Yard.
Earlier, Mr. Trump first responded to the attack in a tweet.
The Metropolitan Police echoed the Prime Minister's concerns, as Mr Trump's comments did not correspond with any information released by the United Kingdom authorities.
Trump referred to the potential attacker as "another loser terrorist."
The manhunt for the terrorist who placed the homemade bomb, which only partially exploded, on the subway train is underway while the investigation into the attack continues. That's because they used knives and a truck! Photos showing crime scene evidence appeared in USA media; the bombing suspect's name was revealed while British officials were still withholding it. Trump said May was "very angry" over the leaks.
Police are today 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 New York Times then published detailed photographs taken from the bomb scene which had been taken by British investigators.
Londoners will never be intimidated or defeated by terrorism.
Sadiq Khan, the Muslim mayor of London, said that his city "utterly condemns the ugly individuals who attempt to use terror to harm us and destroy our way of life".
"I've simply been too busy this morning to look at my Twitter", he told LBC Radio.
British Prime Minister Theresa May said on Friday it was not helpful for anyone to speculate on investigations after U.S. President Donald Trump tweeted that the culprits behind a train bombing had been "in the sights" of the police.
"I'm absolutely not going to go there James, my priority is making sure that we do what we can to keep Londoners safe". I want to know the facts....