A colleague told The Times: "Lukasz grabbed a nearby pole and ran at him, getting stabbed in the hand in the process but continued to pin him down".
"We've taken a lot of action as you can imagine in the last 48 hours".
The Metropolitan Police have named the man and woman who died in the terrorist attack near London Bridge on Friday as Jack Merritt, 25, of Cottenham, Cambridgeshire, and Saskia Jones, 23, of Stratford-upon-Avon, Warwickshire.
Video shot by a witness shows one man chasing Khan with what appears to be the tusk of a narwhal, a large marine animal similar to a whale, while another man sprays a fire extinguisher to distract the knife-wielding Khan.
Police on Saturday were reportedly searching a property in Stafford, in central England, thought to be connected to Khan.
In 2008, Khan's home in Stoke-on-Trent was raided as part of a counter-terrorism investigation.
Khan was convicted in 2012 for his part in an al-Qaeda-inspired plot to blow up the London Stock Exchange and sentenced to indeterminate detention, with a minimum jail term of eight years.
He was released from prison a year ago but had to wear an electronic monitoring device.
He added that there were 74 other convicted terrorists now on the streets who have also been released early, and he promised to toughen their monitoring.
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"We don't think that it is the case that they should all necessarily be released, we think for some offences they should be imprisoned for life, and we also think that terrorist offenders should serve their full sentence".
Johnson reiterated his view when visiting the scene of the attack.
One of the two people he killed was Jack Merritt, 25, coordinator of a reintegration program of the Institute of Criminology at Cambridge, British media reported.
Stephen Toope, the vice-chancellor of Cambridge University said he was "devastated to learn that today's hateful attack on London Bridge may have been targeted at staff, students and alumni attending an event organized by the University of Cambridge's Institute of Criminology".
"My son, Jack, who was killed in this attack, would not wish his death to be used as the pretext for more draconian sentences or for detaining people unnecessarily", wrote David, "R.I.P. Jack: you were a lovely spirit who always took the side of the underdog", reported The Sun.
"We don't need knee-jerk reactions", he added in a series of messages responding to the political furor around the attack.
However, Khan was released early.
Mr. Corbyn rejected the criticism and said the government had made deep cuts to services that help prevent terrorism. "We are all less safe as a result".
The attack brought a somber tone to a rancorous election campaign, which is presenting voters with a stark choice between Labour, with its promise to raise taxes on the rich and businesses to fund a much expanded state, and the Conservatives' pledge to "get Brexit done" and move on to other issues.
He would not commit to ending early release in all scenarios for terrorism offences.
He said: "I think there has to be an examination of how our prison services work and crucially what happens to them on release from prison because I need to know whether or not the Parole Board were involved in his release, apparently they were not, they made that statement quite quickly after the release... after yesterday's bad incident".