"I think if we're frank on both sides of the House [of Commons], we have not done enough to deal with the promotion of extremist Islamism in our own country," he told lawmakers, referring to all political parties.
News that a suicide bomber who attacked a busy shopping street in Stockholm on Saturday had studied and lived in Britain has raised fresh soul-searching here about how to combat radicalism, five years after four home-grown bombers attacked the London transport system in 2005, killing 52 people.
"Whether it's making sure that imams coming over to this country can speak English properly, whether it's making sure we deradicalise our universities, I think we do have to take a range of further steps and I'm going to be working hard to make sure that we do this," Cameron said.
"Yes, we have got to have the policing in place, yes we've got to make sure we invest in our intelligence services, yes we've got to cooperate with other countries. But we've also got to ask why it is that so many young men in our own country get radicalised in this completely unacceptable way," he added.
The man responsible for Sweden's first-ever suicide bombing is believed to have been Taimour Abdulwahab, who until recently had lived in Luton, northwest of London.
He was carrying a cocktail of explosives, but succeeded in killing only himself accidentally on Saturday afternoon near a busy Stockholm pedestrian shopping area.
The man killed himself before he could carry out what, according to the lead prosecutor on the case, appears to have been a mission to murder "as many people as possible." Two others were injured when his car exploded nearby minutes earlier.
Media described the man as an Iraqi-born Swede, although Swedish security service Säpo did not confirm his country of origin, only saying he was from the Middle East and became a Swedish citizen in 1992.
Abdulwahab left the small Swedish town of Tranås three hours southwest of Stockholm in 2001 to study in the British city of Luton. He had been living there with his wife and three children until only weeks before the attack.
The chairman of a mosque in Luton where he used to worship said he had stormed out in 2007 after a series of confrontations over his extremist opinions and had not been seen since.
An Islamist website, Shumukh al-Islam, posted a purported will by Abdulwahab in which said he was fulfilling a threat by Al-Qaeda in Iraq to attack Sweden.