Her remarks come a day ahead of the launch of the government's revised strategy to stop the growth of home-grown extremists.
"For too long there's been complacency around universities," May said.
"I don't think they have been sufficiently willing to recognise what can be happening on their campuses and the radicalisation that can take place. I think there is more that universities can do."
The Daily Telegraph said the "Prevent" strategy would name 25 British boroughs considered most at risk from extremism, including parts of cities like London, Birmingham, Manchester, Leeds and Bradford.
The broadsheet said the revised strategy would contain details of partnerships with video site YouTube and web portal AOL aimed at combating extremism online, as well as moves to limit access to extremist websites from schools and public libraries.
The Daily Mail newspaper said it had seen the updated strategy, which has identified 40 universities where there could be a "particular risk of radicalisation or recruitment".
"More than 30 percent of people convicted for Al-Qaeda-associated terrorist offences in the UK... are known to have attended university or a higher education institution," the newspaper quoted the report as saying.
Taimour Abdulwahab, who blew himself up in Stockholm in December, studied sports therapy at the University of Bedfordshire, north of London.
Investigators believe Nigerian student Umar Farouk Abdulmutallab, who tried to blow up a US-bound airliner on Christmas Day 2009 with explosives in his underwear, was radicalised while studying at a university in London.
Prevent, adopted four years ago following the July 2005 London bombings, is aimed at countering extreme Islam by supporting mainstream Muslim groups.
May launched a review of the strategy in November, saying it was not working as well as it could. The programme cost £60 million ($100 million, 67 million euros).
May said the government would withdraw funding from around 20 out of 1,800 organisations that have received money over the past three years.
The minister was in northern France on Monday for talks with her French counterpart on tackling illegal immigration.
-----------------------------------------------------------------------------------
"For too long there's been complacency around universities," May said.
"I don't think they have been sufficiently willing to recognise what can be happening on their campuses and the radicalisation that can take place. I think there is more that universities can do."
The Daily Telegraph said the "Prevent" strategy would name 25 British boroughs considered most at risk from extremism, including parts of cities like London, Birmingham, Manchester, Leeds and Bradford.
The broadsheet said the revised strategy would contain details of partnerships with video site YouTube and web portal AOL aimed at combating extremism online, as well as moves to limit access to extremist websites from schools and public libraries.
The Daily Mail newspaper said it had seen the updated strategy, which has identified 40 universities where there could be a "particular risk of radicalisation or recruitment".
"More than 30 percent of people convicted for Al-Qaeda-associated terrorist offences in the UK... are known to have attended university or a higher education institution," the newspaper quoted the report as saying.
Taimour Abdulwahab, who blew himself up in Stockholm in December, studied sports therapy at the University of Bedfordshire, north of London.
Investigators believe Nigerian student Umar Farouk Abdulmutallab, who tried to blow up a US-bound airliner on Christmas Day 2009 with explosives in his underwear, was radicalised while studying at a university in London.
Prevent, adopted four years ago following the July 2005 London bombings, is aimed at countering extreme Islam by supporting mainstream Muslim groups.
May launched a review of the strategy in November, saying it was not working as well as it could. The programme cost £60 million ($100 million, 67 million euros).
May said the government would withdraw funding from around 20 out of 1,800 organisations that have received money over the past three years.
The minister was in northern France on Monday for talks with her French counterpart on tackling illegal immigration.
-----------------------------------------------------------------------------------