"It would be the height of folly to believe that the Iranian regime can be our partner in managing the deteriorating security situation in Iraq," said McCain in a statement.
“We’re open to discussions if there is something constructive that can be contributed by Iran, if Iran is prepared to do something that is going to respect the integrity and sovereignty of Iraq,” he said.
Appearing on the Sunday news shows, Graham cautiously endorsed the idea, provided certain conditions are met.
"Well, we're going to probably need their help to hold Baghdad," he said on CBS News's "Face The Nation."
On the same program, Graham said, "We need to all make sure Baghdad doesn't fall. So, yes, we need a dialogue of some kind with the Iranians, but we also need to put them on notice. Don't use this crisis as a way to create a satellite state of Iraq controlled by Iran."
McCain said the "reality" of the situation "is that U.S. and Iranian interests and goals do not align in Iraq, and greater Iranian intervention would only make the situation dramatically worse."