Assembly parties have united to voice grief and anger at the terrorist attacks in Tunisia, France and Kuwait.
The Isis-linked incidents across three continents, which have led to more than 60 deaths so far, were raised as an urgent matter of the day by sole Ukip MLA David McNarry.
He said the attacks last Friday had "shook the free world".
He went on: "It is unforgivable. Islamic countries must now decide to disown IS, to reject and repudiate it. They cannot host tourists and harbour terrorists at the same time. Our Government must also act by informing us all of the level of threat existing in our United Kingdom. I trust that the House will unite in that condemnation."
Alliance's Stephen Farry said he would differ with Mr McNarry because he believed very few states in the world are actively harbouring Islamic State.
"Islamic State is as much a threat to the states in the Middle East as to ourselves here in the west. People referred to Tunisia, which is now suffering hugely in terms of the loss to its economy," Mr Farry added .
Former DUP minister Sammy Wilson said leaders in the Muslim community in Northern Ireland also need to bear their own responsibility in mind.
"It was not so long ago that we heard the head of the Muslim community in Northern Ireland on the radio actually praising this death cult for what it had done when it took over Mosul, and claiming that it had brought order to that city," he said.
"When people are considering how we deal with this, everyone, especially those within the Muslim community, have to ask themselves what responsibility we have if our families are being drawn into this."
Sinn Fein's Caitriona Ruane argued: "The vast majority of people from the Muslim world, here in Ireland and across the world will also be horrified and reject the activities of Isis.
"The onus is on us to reach out to progressive and representative voices to address the issues that allow that sort of extremism to exist."