Iraq's fractious parliament met Sunday and again failed to make any progress toward forming a new government, even as militants gained ground north of Baghdad in a renewed drive.

World powers and Iraq's top Shiite cleric, Grand Ayatollah Ali al-Sistani, have been piling pressure on MPs to put aside their differences, with the country facing a major jihadist-led onslaught that has overrun chunks of five provinces.

But "no type of agreement was reached... between the various blocs" at Sunday's session, which was adjourned to Tuesday, acting parliament speaker Mahdi Hafez announced.

The latest stalemate came despite the announcement late Saturday of an agreement among Sunni Arab lawmakers on a candidate for speaker, a post traditionally held by the minority group that must be filled before the government formation process can go ahead.

Parliament's United for Change, a Sunni grouping, said Dr Salim al-Juburi had been selected, but it went on to pledge not to accept incumbent premier Nuri al-Maliki for a third term.

Former parliament speaker Osama al-Nujaifi called on Sunday for a vote on Juburi's candidacy, but Hafez refused, saying not all blocs were in agreement, though there were more than enough MPs present to hold a vote.

The UN's Iraq envoy, Nickolay Mladenov, had warned that "failing to move forward on electing a new speaker, a new president and a new government risks plunging the country into chaos".

"It will only serve the interests of those who seek to divide the people of Iraq and destroy their chances for peace and prosperity."

Sunday's session was the second time parliament has completely failed to make progress.

A July 1 meeting broke down when MPs traded barbs and enough failed to return after a break that the legislature was left short of a quorum.

- Militants gain ground -

As the highly paid deputies kept up their squabbling, militants launched a renewed push, seizing two towns northeast of Baghdad, while major attacks west of the capital were stymied by security forces and allied tribesmen.

Militants attacked the town of Dhuluiyah, just 80 kilometres (50 miles) north of Baghdad, overrunning more than half of it and bombing three police stations, the local council headquarters, a court and a bridge, officials said.

Six people, among them four policemen, were killed in the violence.

Bombings and shelling in the Baghdad area and Diyala province killed at least six more people, including a police brigadier general, officials said.

Despite calls for a new government to help counter the militant offensive, prospects appeared dim for any speedy resolution of seemingly intractable differences over key appointments and other issues.

Ties between the Baghdad government and Iraq's autonomous Kurdish region have hit a new low, and Maliki has pledged to seek a third term despite some lawmakers insisting he step aside.

On Friday, the Kurdish region's government claimed disputed northern oilfields, having earlier taken control of other contested areas abandoned by Iraqi forces last month as they fled a sweeping offensive led by the jihadist Islamic State (IS) group.

Kurdish regional president Massud Barzani has also called for a vote on outright independence, further souring ties with the federal government.

Kurdish lawmaker Rizan Diler Mustafa told AFP before Sunday's session that he thought it would "be the same as the previous one. I doubt the parties will reach agreement on the three nominees."

- Divisive PM -

Under an unofficial agreement, the posts of speaker, president and prime minister are allotted to a Sunni Arab, Kurd and Shiite Arab, respectively.

Maliki has accused the Kurds of exploiting the insurgent offensive and harbouring militants, while the Kurds say Baghdad is unfairly withholding their share of oil revenues and have called for him to step down.

Maliki, a Shiite Arab viewed by opponents as a divisive and sectarian leader, has no plans to do so, despite eroding political support and thinly veiled calls for change from Washington.

The 64-year-old premier and his coalition partners dominated elections in April, and there is no obvious consensus candidate to replace him.

In a sign of Washington's concern, Vice President Joe Biden Saturday spoke by phone with Barzani and Nujaifi about the need for "all Iraqi political forces" to work to form a new government as soon as possible, the White House said.

It is hoped a new more inclusive government will help drain resentment among Iraq's minority Sunni Arabs that plays into the hands of militant groups.