Some leaders of Iraq's Sunni Muslim minority have said they may work with the new prime minister, a move that could help breakpolitical deadlock.
The mainly Shia Muslim government is locked in a fight with Islamic State (IS), an extreme Sunni group leading an insurrection in the north.
Fighting has flared up in mainly Sunni Anbar province, west of Baghdad, parts of which have been under IS control.
In New York, the UN slapped sanctions on IS and another group.
The Security Council unanimously passed a resolution naming six people associated with IS or the Syria-based Nusra Front, who will be subject to an international travel ban, asset freeze and arms embargo.
It also threatened sanctions against those who finance, recruit or supply weapons to the militants.
Earlier, the EU condemned IS "atrocities and abuses" against religious minorities.
Christian and Yazidi people in northern Iraq have faced persecution by the jihadists, prompting US-led air strikes and aid drops.
In an emergency meeting of the 28 EU states in Brussels, the countries were left to decide individually whether they would arm Iraq's Kurds, the main opponent of IS in the north.
IS-led violence has driven an estimated 1.2 million Iraqis from their homes. Whole communities of Yazidis and Christians have been forced to flee in the north, along with Shia Iraqis, whom IS do not regard as true Muslims.
Grand Ayatollah Ali al-Sistani, Iraq's most influential Shia cleric, threw his weight behind the new Iraqi prime minister on Friday.