Odin

I think the out is travel to a place where the government says you should not go might not be covered by travel insurance. That is normally how it works. It warns against all but essential travel to Iraq. That warning has probably been in place for a long time, with extra restrictions placed during June 2014. I am going by what my own travel policy says as an example, what does the Travelguard one state in the small print? What countries have been excluded from cover, usually it is countries such as Afghanistan, Sudan, Iraq etc? As the US Travel advice page says, those who still want to travel will have to take responsibility for their own security.
As for not being a US citizen, citizenship doesn't matter but residency does. If you are not a US resident, you need to select your country from the dropdown list. If it is not on the list, you need to be calling the insurance company.

Milletali1986

so i have gotten a refund on the tickets for July 15th. i got the refund actually through the airline they said we see the travel warning that has been posted. i am still fighting with the insurance company for the June 28th tickets. and yes i am a US citizen.

NewbE

Good! Glad to hear you're halfway there and hope you will succeed in getting the other tickets refunded as well.