Senior Tory sources said a derogation from the laws could be used.
"As we see the threat changing, evolving, becoming more complex, we need to ensure that our police and our security and our intelligence agencies have the powers they need", May said at a campaign stop in Slough.
"We should have longer prison sentences for people convicted of terrorist offences".
The prime minister said she meant to enact "longer prison sentences for people convicted of terrorist offences ... making it easier for the authorities to deport foreign terror suspects to their own countries [and] doing more to restrict the freedom and the movements of terrorist suspects when we have enough evidence to know they present a threat, but not enough evidence to prosecute them in full in court".
Asked about the prime ministers proposal, the Liberal Democrat leader said: "When all is said and done, changing the law is not what keeps us safe".
Metropolitan Police Assistant Commissioner Mark Rowley said police and their partners are "doing everything we can across the country to help prevent further attacks and protect the public from harm".
May replaced Control Orders with Terrorism Prevention and Investigation Measures (TPims), which require suspects to stay overnight in an address for up to ten hours - but it might not necessarily be their home.
Both the Conservative and Labour parties, the U.K.'s largest parties, suspended campaigning Monday in the wake of London terror attack.More news: Kohli hosts charity ball in London amidst Champions Trophy campaign
The security services have come under pressure after it emerged one of the attackers, Khuram Butt, 27, had been reported to the anti-terror hotline in 2015. Setting out how she'd spend Britain's clawed-back contributions to the European Union budget as the country leaves the bloc, she said there'd be more money for fast internet connections, funds to commercialize research, and better road and rail services as part of a 23 billion-pound ($29.7 billion) package.
"And responsibility for that lies squarely with Theresa May and her dereliction of duty".
But the Foreign Secretary dismissed the idea that cuts to police numbers could be responsible, despite jibes from Labour.
"All she would do is reduce freedom, not terrorism".
Liberty director Martha Spurrier said: "If Theresa May does what she threatens, she will go down in history as the prime minister who handed terrorists their greatest victory".
It is not clear whether this toughening of stance will do her any good or not as her opponent Jeremy Corbyn has been able to gain support for linking these terrorist attacks to foreign interventionist policies of the United Kingdom, which have been pursued for years. We have had three horrific attacks and we have foiled five others.
Mrs May has come under fire since the attack, with Labour leader Jeremy Corbyn calling for her resignation over her record on police cuts.