Some leaders of Iraq’s Sunni Muslim minority have said they may work with the new prime minister, a move that could help break political 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.
Chink of hope
A group of leaders from restive Sunni provinces issued a joint statement addressed to new Iraqi Prime Minister Haider al-Abadi, who took over from Nouri Maliki on Thursday.
They said they could join the new government if the security and civil administrations in their areas were given equal status to that of the central government.
But they demanded that the Iraqi authorities stop the bombardment of Sunni provinces and cities, and said that local people should be allowed to run Sunni provinces.
Calling for a reform of the Iraqi army, they asked for the release of political detainees, an end to executions and the withdrawal of militias from Sunni cities.
Analysis: Jim Muir, BBC News, northern Iraq
In order to drive a wedge between Iraqi nationalist Sunnis and Islamic State, the Iraqi Sunnis must first be won over – not only by giving them seats in government, but by empowering them in their own areas.
Many have said they would then turn on the Islamist radicals and there are signs that it may have started to happen in some areas.
In 2007 the Sunnis drove al-Qaeda out of western Iraq altogether. This will be a much tougher affair.
If it is to stand a chance, the Sunnis will need all the help they can get from Iraqi government troops, Kurdish Peshmerga forces and American airpower. Nor can it really start in earnest until a solid new power-sharing deal is struck in Baghdad.
A source in Anbar province told the BBC’s Arabic Service that the statement had been written by a group of Sunni leaders from six provinces and had been approved by “revolutionary tribesmen and military councils”.
Separately, one of the most powerful Sunni tribal leaders, Ali Hatem Suleiman, said he was ready to work with the new prime minister, provided he protected the rights of the minority.
A decision on whether or not to fight IS would come later, he added.
The removal of Mr Maliki, who was hated by the Sunnis, has provided a chink of hope in Iraq’s crisis, BBC World Service Middle East editor Sebastian Usher reports.
There is no doubt that Sunni tribes are essential to any solution, but it will take a great deal to restore any of their trust in central government, he says, noting that other Sunni leaders have already dismissed the political transition as all but meaningless.
Fighting flared up on Friday with IS militants in Anbar.
AFP news agency quoted a Sunni tribal leader, Sheikh Abduljabbar Abu Risha, as saying an “uprising” was under way against IS, while Anbar police chief Maj-Gen Ahmed Saddak said security forces were backing the fight to drive out IS.
Air bridge plan
In a statement, the EU ministers said: “The EU remains seriously concerned about the deterioration of the security situation in Iraq, and condemns in the strongest terms the attacks perpetrated by [IS] and other associated armed groups.
The UK said it would “consider favourably” any request to send arms to the Kurds, while the Czech government said it would be in a position to start deliveries of munitions by the end of the month.
Germany is legally prevented from arming countries involved in conflict, but Foreign Minister Frank-Walter Steinmeier said he would go to the limit of “what is legally and politically possible” to help the Kurds and he will travel to Iraq shortly.
The EU ministers agreed to provide a humanitarian air bridge to help those refugees driven from their homes, but there was little detail as to the funding or the timetable, BBC Europe editor Gavin Hewitt reports.
The British government said two planeloads of aid were on their way to Irbil, destined for the Dahuk refugee camp.