The Met Police said their names would be released "as soon as operationally possible" as officers work to establish if they were part of a wider network.
They were shot by police after driving into pedestrians on London Bridge and stabbing people in Borough Market.
Officers searched two addresses in east London on Monday morning.
Police said a "number of people" had been detained following the raids, in Newham and Barking.
It comes after 12 people were arrested in Barking on Sunday following raids at a flat - believed to be the home of one of the attackers. A 55-year-old man has since been released without charge.
Metropolitan Police Commissioner Cressida Dick said a "huge amount" of forensic material and evidence had been seized from the van and police raids.
She told BBC Breakfast the investigation was moving very quickly and the priority now was to establish if anybody else was involved in the plot.
The so-called Islamic State group has claimed responsibility for the attack.
Chrissy Archibald moved to Europe to be with her fiancé
The first victim of the attack has been named as Canadian national Chrissy Archibald.
A statement from her family said she had worked in a homeless shelter until she moved to Europe to be with her fiancé.
A French national was also killed in the attack, according to foreign minister Jean-Yves Le Drian.
London Bridge rail and Tube stations both reopened for entry and exit early on Monday morning, after National Rail said the police cordons in the area of the attack had been lifted earlier than expected.
The bridge and surrounding roads have also reopened.
Two people have also claimed they had warned the police about the behaviour of one of the attackers.
Speaking to the BBC's Asian Network, an unnamed man said one of the attackers had become more extreme over the past two years.
'I did my bit'
"We spoke about a particular attack that happened and, like most radicals, he had a justification for anything - everything and anything.
"And that day I realised that I need to contact the authorities," he said.
He said no action was taken.
"I did my bit... but the authorities didn't do their bit".
Police carried out raids in east London after Saturday's terror attack in the capital
Speaking on Sunday, Metropolitan Police Assistant Commissioner Mark Rowley said 36 people were in hospital with a "range of injuries" and 21 were in a critical condition.
Four police officers were among those injured, two of them seriously.
Australian Prime Minister Malcolm Turnbull has confirmed four of the country's nationals had been caught up in the attack.
Two, Candice Hedge from Brisbane and Andrew Morrison from Darwin, are among the injured after both were stabbed.
Seven French nationals were injured in the attack, including four with serious injuries, while one French national is still missing
Eyewitnesses described it travelling at high speed, hitting pedestrians, before crashing close to the Barrowboy and Banker pub.
The van had recently been hired by one of the attackers, Mr Rowley said.
It is the third terror attack in the UK in three months, following the car and knife attack on Westminster Bridge in March, in which five people were killed, and the Manchester bombing less than two weeks ago, in which 22 people were killed.
Prime Minister Theresa May condemned the attack, saying it was "time to say enough is enough" and end the UK's "tolerance" of extremism.
She said full campaigning would resume on Monday after most political parties suspended general election campaigning on Sunday.
She confirmed Thursday's election would go ahead as planned.
In a speech, Labour leader Jeremy Corbyn backed the police to use "whatever force is necessary" to save lives.
A new normal?
With three attacks in three months, terrorism against soft targets is beginning to feel, to some people, like the new normal.
The brutal reality is that this kind of threat is absolutely typical of what jihadists sought to achieve in all their attacks across Europe.
Since 2013 security services in the UK have foiled 18 plots. A large proportion of those have involved suspects who set out to commit acts of violence similar to the attacks on Westminster Bridge and London Bridge.
Plans to use bombs, such as at Manchester Arena, are rarer because plotters need to have the technical skills for such an appalling attack - but attacking people with cars and knives is far easier and has long been encouraged by so-called Islamic State and other jihadists.
The aim of the three attackers last night is abundantly clear - not only did they want to kill, but they wanted to lose their own lives.
They would have known full well that attacking people in the street would draw armed police in their direction and the fake bomb belts they were wearing would, in their own warped minds, hasten their demise.