The top UN official in Baghdad has urged the West to encourage Iraq's political groups to form a new government in line with the constitution and help them overcome sectarian tension.

U.S. Secretary of State John Kerry has said Iraqi Prime Minister Nouri al-Maliki told him he would meet a July 1 deadline to form a new inclusive government, but the blocs are divided over how to proceed after an election two months ago, faced with a war against Sunni militants.

Meanwhile, nearly half of the roughly 300 U.S. military advisers and special operations forces expected to go to Iraq arrived in Baghdad to assess Iraqi forces in the fight against Sunni militants, the U.S. Defence Department said.

On Capitol Hill, senators who left a closed briefing with senior Obama administration officials expressed hope Iraq could soon form a new government, perhaps in the next week, facilitating greater U.S. military action against the Islamic State of Iraq and Syia (ISIS).

At the Pentagon, Navy Rear Adm. John Kirby told reporters the troops in Baghdad included two teams of special forces and about 90 advisers, intelligence analysts, commandos and support personnel needed to set up a joint operations centre in the Iraqi capital.

Another four teams of special forces are set to arrive in Baghdad in the next few days, Kirby said.

Those troops, added to the approximately 360 other U.S. forces in and around the embassy in Baghdad to perform security, would bring the total U.S military presence in Iraq to about 560.

Militants mining deep resentment: UN

At least a 1,000 people have been killed in fighting and other violence in Iraq in June alone as Sunni Islamists from the Islamic State in Iraq and Syria sweep through the north, the United Nations said on Tuesday.

Nickolay Mladenov, head of the UN political mission in Iraq, said Western governments should push the parties to stick to the deadline for forming a government.

According to the constitution, parliament's first session should be held within 15 days of the ratification of the result by the federal court, which took place last week.

"A new parliament is supposed to meet so we need to encourage that everyone stays within that framework," Mladenov told Reuters on the sidelines of a meeting of EU foreign ministers in Luxembourg late on Monday.

Mladenov said the European Union should also take advantage of its experience in dealing with ethnic divisions and set up a long-term plan to help Iraq overcome sectarian strife.

The militants are exploiting deep resentment among Iraq's Sunni minority, which lost power when the 2003 U.S.-led invasion toppled Saddam Hussein. Since the U.S. withdrawal in 2011, the Sunni population has become increasingly alienated from Maliki's Shia-dominated government and his U.S.-trained military.

Mladenov reiterated his assessment that Baghdad was well protected from attack for now, but said the capital could come under threat if the conflict intensifies.

"What I would see as a game-changer is if the city is surrounded by ISIS from the south as well as the north. But at this point it is quite well protected," he said.