The U.S. administration is indicating it wants Iraq’s political parties to form a new government without Mr. Maliki as he tries to assemble a ruling coalition following elections this past April, U.S. officials say.

Such a new government, U.S., officials say, would include the country’s Sunni and Kurdish communities and could help to stem Sunni support for the al Qaeda offshoot, the Islamic State of Iraq and al-Sham, or ISIS, that has seized control of Iraqi cities over the past two weeks. That, the officials argue, would help to unify the country and reverse its slide into sectarian division.