I do not remember which banks but some Iraqi banks I have
previously contacted responded quite promptly surprisingly
despite all the situations there to my inquiries so anyone
interested in opening the account might want to write
to the banks directly as well. I have not proceeded in
opening the account though. List of the banks below
though it may be outdated now, could still be useful
for searching banks.
http://www.cpa-iraq.org/economy/iraq_private_banks.html