Mrs May warned the threat from Islamic state was moving “from the battlefield to the internet” as she led sessions on counter-terrorism in Taormina in Italy.
In the wake of the Manchester bombing the PM and her counterparts agreed a series of measures to step up the fight against terror and backed her call for more pressure to be put on internet companies such as Google, Facebook and Twitter to target extremist content.
But she was forced to defend her record on tackling violent extremism in the face of police cuts and the failure to stop jihadi fighters returning to Britain.
Mrs May described the G7 joint statement as “a significant step forward”, and said she wanted to see terrorist material taken down “more urgently and more rapidly than it is at the moment”.
She added: “It is also the case that I think it’s important that companies recognise their social responsibility and do report matters that they become aware of to the authorities.
“We need to work together to fight against the evil of terrorism. And nobody can be in any doubt, after what we saw in Manchester, of just how evil those terrorists are.”
However, she denied cutting police numbers by 20,000 had made it necessary to put troops on to the streets in the wake of the atrocity.
She told a press conference at the summit: “The plan to ensure that there was military support available to the police is a well-prepared plan, it’s one that was developed a while ago.
‘It was done so that at a time when we got to ‘critical’ in our threat level – which of course is determined independently by the Joint Terrorism Analysis Centre – extra support could be made available. And that is exactly what has happened.”
Mrs May was also asked by Sky News if she had “dropped the ball” as home secretary, given figures that showed 400 foreign fighters had returned to the UK since 2014.
The PM said: “It is the case that we believe a number of foreign fighters who went to Syria have returned to the UK.
“We actually took some extra powers in legislation when I was home secretary to manage the return of individuals, and those are looked at on a case-by-case basis.
“Over the last six to seven years, I excluded more hate preachers from the United Kingdom than any home secretary has ever done before. We did not hesitate to act in protecting our national security.”