On June 5, London police said they carried out fresh raids and detained an undisclosed number of people in the investigation into the attack.
"The police are working hard to establish the identity of all those who were tragically killed or injured in the event on Saturday night", May added.
Jeremy Corbyn, leader of the main opposition party, called on May to resign over the issue, saying earlier that "you can not protect the public on the cheap", and promising to recruit another 10,000 police officers if he is elected into power.
The attack, the third in Britain in three months involving suspects who had been on the radar of British authorities, has raised questions over the government's ability to protect Britain following cuts to police numbers in recent years.
Police disclosed late on Monday that 27-year-old Khuram Butt, a British citizen born in Pakistan, was known to police and domestic spy agency MI5 but with resources scarce had not been deemed enough of a threat to warrant close monitoring. The other suspect, 30-year-old Redouane, claimed to have roots in Morocco and Libya.
In total 15 men have arrested as part of the investigation, with 12 of those released without charge.
Dick said police had seized "a huge amount of forensic material" after going through the van used in the attack "very very carefully". "We will do our very best to try and keep them safe", he told local media.
A tearful woman has paid tribute to her brother, who was the second London terror attack victim to be identified. We continue to unite against those who seek, through violence and extremism, to intimidate or cause fear. "You will not win", Khan said to applause. The Islamic State group has claimed responsibility.
Health authorities said 10 were in a critical condition. One of the properties was believed to be the home of one of the attackers.
Armed police responded and within eight minutes had shot dead all three attackers. "One whole day", she said.
In its wake, the message sent by many Londoners, including those who survived the attack, was one of solidarity.
Asked by ITV television if he backed the calls for May to resign, he said: "Indeed I would".
Corbyn has pledged to hire thousands of officers for neighbourhood duties, arguing that a grassroots approach would curb crime and radicalisation.
Grande headlined a benefit concert in the northwestern city on Sunday, alongside stars including Pharrell Williams and Justin Bieber. Our work necessarily involves making hard judgments about how to prioritize the resources available to us at a time when the United Kingdom is facing a SEVERE and high tempo terrorist threat. Seven people died and dozens were wounded during the attack late Saturday.