“There is a new political map,” said Anwar al-Luheibi, a Sunni adviser to Maliki, who is a Shiite. “And I anticipate this map will be far better than the one we had before.”

The negotiations and deal-making mark a departure from politics that have hewed almost exclusively to ethnic and sectarian lines, fomenting the discord that brought Iraq to the precipice of civil war in 2006 and 2007. They represent the first round of a great game that may resolve a question unanswered since Saddam Hussein’s fall in 2003: What coalition of interests will find the formula to wield power in Iraq from Baghdad?