Pamela Geller, the organiser of a controversial Texas competition of cartoons of the Prophet Mohammed and radical Muslim Imam Anjem Choudary clashed on Fox News.
In the encounter on the Sean Hannity slot, Choudary appeared to condone alleged death threats made against controversial anti-Islam blogger Geller by an Isis supporter on Twitter, after she organised the event in Garland, where two gunmen attempting to attack the competition on Sunday, May 3, were shot dead.
"You're talking about people who deliberately had a competition to insult the messenger Muhammad," said Choudary, former spokesman of banned group Islam4UK, which advocated the establishment of strict sharia law in the UK.
"Let's be clear we are not talking about Mickey Mouse or Donald Duck. We are talking about people who deliberately had a competition to insult the messenger Muhammad.
"If you saw the cartoons that Charlie Hebdo drew, you would understand the anger," he said.
When challenged by Hannity, Choudary did not deny that he supported calls for Geller to be killed.
"She should be put before a Sharia court and tried and, if guilty, face capital punishment," he said.
Geller blamed US President Barack Obama for creating "an environment that raised the stakes" on Islamic extremism in America.
Despite Choudary's attempts to interrupt her she said, "I know you are used to stepping over women, but you're not going to have it here.
"To blame me and say that my cartoons are controversial? Murdering cartoonists is controversial," she said, before blaming Sharia law for widespread slaughter.
"Under the Sharia they are slaughtering the Christians and secular Muslims across Africa and across the Muslim world," she said.
Geller has been accused of stirring up Islamophobia, and she defended her decision to hold the competition.
"I submit to you that my conference saved lives because I understand the threat, and we had enormous protection, and the Garland Police were superb," she asserted.
Neither Geller nor Choudary are strangers to controversy.
Geller is the founder of think tank the American Freedom Defense Initiative, which has been branded a hate group by the Southern Poverty Law Centre in the US, and regularly publishes anti-Islam material.
In 2013, she was denied entry to the UK along with fellow anti-Islam blogger Robert Spencer where she was due to address a rally by the far-right EDL group.
The UK anti-racism group Hope Not Hate has described Choudary as "the single biggest gateway to terrorism in recent British history," and claims he has facilitated and encouraged many UK Muslims to join radical Islamist groups including Isis fighting in Syria.
Heidi Beirich, the director of the SPLC's Intelligence Project condemned Fox News for allowing the encounter between the extremists to take place.
"We're disappointed, but not entirely surprised, that Sean Hannity would offer a national platform to two well-known haters. Ms Geller and Mr Choudary represent nothing more than an extreme political fringe.
"Their divisive behavior is made even worse by the fact that Ms Geller is now positioning herself to be a defender of free speech, while Mr Choudary is purporting to speak on behalf of all Muslims."