The family of Kayla Mueller, who was killed while held captive by Islamic State in Syria after travelling to the region to do humanitarian work, have said that they believe there was a chance  she could have been released.

They also said that they believe the US government "waited too long" before launching a rescue attempt.

Speaking on NBC News' Today programme, Kayla's father Carl said the rescue attempt last July, which saw US commandos raid an abandoned oil refinery where hostages were believed to be held, was a mistake.

"You don't want to put soldiers in harm's way without knowing exactly the circumstances," he said. "But yeah, I think they waited too long. Through people that have gotten released, we had an idea of where they were. And it was 30 days, I think, before they took action."

The family also said that the deal struck with the Taliban for US soldier Bowe Bergdahl, apparently captured after walking off his base having expressed doubts about his role, had made negotiations with Islamic State more difficult.

IS had been in contact with the family and asked for $6.2 million, which was beyond their resources. "I really feel that we had a chance to get Kayla out," Carl Mueller said. "We were in communications with them, unlike other families. But how do you raise $6.2 million? You know, it pretty much made it impossible."

The Muellers said communication with their daughter's captors fell apart with news of Bergdahl's exchange for five prisoners.

Kayla's brother Eric said: "That made the whole situation worse, because that's when the demands got greater. They got larger. They realised they had something. They realised that, 'Well, if they're gonna let five people go for one person, why don't they do this? Or why don't they do that?'"

Carl Mueller also said he had mixed feelings about the government's refusal to negotiate with terrorist groups who kidnapped foreigners.

"We understand the policy about not paying ransom," he said. "But on the other hand, any parents out there would understand that you would want anything and everything done to bring your child home. And we tried. And we asked. But they put policy in front of American citizens' lives."

Asked whether the government did enough to help Kayla, Mueller's mother Marsha replied: "​I think they wanted to. But I think again, it's the policy. And I don't think anyone had any idea this group would be as powerful as they were."

The US, like the UK, has a policy of not paying ransoms, which are a major source of funding for terrorist groups. President Obama told Buzzfeed last year: "The one thing that we have held to is a policy of not paying ransoms with an organisation like ISIL. And the reason is once we start doing that, not only are we financing their slaughter of innocent people and strengthening their organisation, but we're actually making Americans even greater targets for future kidnappings."