The radical Sunni militia that has plunged Iraq into chaos bragged on Sunday that it had executed hundreds of Shiite Iraqi soldiers, even as the Obama administration said it is preparing to open direct talks with Iran on how the two longtime foes can counter the insurgents.

The U.S.-Iran dialogue, which is expected to begin this week, will mark the latest in a rapid move toward rapprochement between Washington and Tehran over the past year. It also comes as the U.S. and other world powers try to reach an agreement with Iran...