Seven people were killed in the assault, which occurred Saturday when three masked men drove a van into pedestrians on the bridge before jumping out and stabbing people at random.
Butt, 27, was a Pakistan-born British citizen who was known to the police.
Naming Butt and an accomplice, police admitted he was known to them and MI5, but that "there was no intelligence to suggest that this attack was being planned and the investigation had been prioritised accordingly".
On Twitter, people using the hashtag #ChrissySentMe expressed their sadness for the family's loss, but many also said they were inspired by the call for meaningful action.
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As the nation collectively grieves following the third terror attack to hit the country in three months, a minute's silence will be observed on Tuesday at 11am in memory of the victims.
Metropolitan Police say that as of Monday evening local time, they had searched six properties and "arrested 12 people - seven women and five men".
Police were not yet releasing the names of the dead, but thousands of people gathered at Potters Field, across from the Tower Bridge and the medieval Tower of London, to pay tribute to the victims.
Joaquin Echeverria wrote on Facebook he had been seen "defending someone with his skateboard", adding: "We keep looking for Ignacio, disappeared in the London attacks".
He is said to be inconsolable and family members are rushing to his side.
The invitation issued by Khan's office says the vigil also is meant to show "We will never let these cowards win and we will never be cowed by terrorism".
UK police reveal names of London attackers, say one investigated before
Asked about Trump's ongoing Twitter tirade against him, Khan added: 'It takes two to tango, and I'm not tangoing with this guy. An Irish security source described the murderer as having "extensive immigration history related to the UK".
She said: 'The Commissioner of the Metropolitan Police has said that the Met is well resourced, and they are, and that they have very powerful counter-terrorism capabilities and they do. A third attacker has not been identified. She could have been any one of us and her tragic death has left our province shaken.
"Whatever the United States can do to help out in London and the U.K., we will be there", Trump wrote. Some of the 48 people injured are in a "critical" condition, London Mayor Sadiq Khan told reporters Sunday in comments broadcast by the BBC.
It comes in the wake of a suicide bombing outside an Ariana Grande concert in Manchester May 22 that killed 22.
He said many people were "very anxious that she was at the Home Office for all this time, presided over these cuts in police numbers, and now is saying that we have a problem". Campaigning resumed Monday after being suspended by major political parties in the aftermath of the attack.
Two London Bridge attackers named
Network Rail said London Bridge rail and London Underground stations reopened at 5am but the rail station will be exit only. The country's major political parties temporarily suspended campaigning with only days to go before the general election.