Security and terrorism policy featured strongly as the Green Party and UKIP leaders faced a Question Time audience.
UKIP leader Paul Nuttall called for 20,000 more police officers on UK streets, and for a review of funding of mosques in Britain.
Green co-leader Jonathan Bartley said the Prevent counter-radicalisation strategy should be scrapped.
The Bristol Q&A was the latest in a series of special shows ahead of Thursday’s general election.
It took place the day after the London Bridge terror attack, which killed seven people and injured 48.
Mr Nuttall, who has previously stated that detention without trial should not be ruled out for terror suspects, said a return of control orders and tagging should also be considered.
“Politician after politician” had refused to acknowledge the problem of radical Islam, he said.
“It’s not about Muslims,” he said, “Islamism is a political ideology”.
But a woman in the audience said he was actually “grouping” all Muslims together with policies like UKIP’s proposed burka ban, and another audience member suggested his comments were fuelling radicalisation.
“We’ve got to say to these people Islamism is not welcome in this country,” Mr Nuttall replied.
Mr Nuttall, who is seeking to gain his party a foothold in Westminster after its sole MP quit the party, also backed the Prevent strategy and called for an investigation into the Saudi funding of UK mosques.
Appearing separately on stage, Green Party of England and Wales co-leader Jonathan Bartley called for a UK arms embargo on Saudi Arabia, but did not support Prevent.
“It is clearly toxic to some communities,” he said.
“It is alienating some communities and therefore we are not getting to the root of radicalisation, not building bridges we need. We are not getting the intelligence that we need.”
Migration and NHS
Mr Bartley, whose party had one MP in the previous Parliament, echoed attacks on cuts to police numbers, saying they threatened the British tradition of community policing and “policing by consent”.
Pressed on whether he would authorise a drone strike on a jihadist overseas, he said he would look at it on a case-by-case basis, but warned: “Those incidents have consequences for radicalisation”.
The two politicians were also quizzed on their wider policies.
These included the Greens’ pledge for a four-day week – Mr Bartley jokingly told the audience it would help them avoid the “Sunday night feeling” and said it would help deal with the effects of “automation” in certain sectors.
Mr Nuttall was asked whether his proposed post-Brexit migration crackdown was a “danger” to the NHS.
He dismissed this, saying the government should assure all EU migrants working in the NHS that they can stay in the UK and calling for the foreign aid budget to be “slashed” to increase funding for the health service.