BAGHDAD (AFP) - Iraq's fractious Parliament elected a speaker on Tuesday, setting the stage for the government formation process to proceed after extensive delays, as security forces advanced into militant-held Tikrit.

World powers and Iraq's top Shi'ite cleric, Grand Ayatollah Ali al-Sistani, had piled pressure on MPs to put aside their differences to help counter a major jihadist-led onslaught that has overrun swathes of territory north and west of Baghdad.

After two sessions in which they made no progress, MPs elected Mr Salim al-Juburi Parliament speaker, a post traditionally held by a Sunni Arab that must be filled before the process of forming a government can go ahead.

Acting Speaker Mahdi Hafez announced that Mr Juburi, an MP from Diyala who ran on an independent list, won 194 of 273 votes cast.

It was not immediately clear if his election was part of a package deal involving the two outstanding senior posts of president and prime minister, but Tuesday's progress after previous deadlocked sessions indicates that some type of accord has been reached.

Lawmakers must now elect a president, who will then give the biggest bloc the first chance to form a government.

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

Earlier on Tuesday, security forces began an attack on Tikrit, aiming to revitalise an operation to retake it that began more than two weeks ago but became bogged down south of the city.

"Iraqi forces began a military operation to liberate the city of Tikrit and our forces were able to control the southern part of the city," Mr Ahmed Abdullah Juburi, the governor of Salaheddin province, of which Tikrit is the capital, told AFP.

An army colonel said the police academy and a hospital had been retaken, and the governor confirmed those facilities were back in government hands, along with the governorate headquarters.

Tikrit was seized by militants on June 11 as part of a sweeping offensive that has overrun large areas of five provinces since it began last month.

Tribesmen and security forces also battled militants in the town of Dhuluiyah on Thursday, just 80km north of Baghdad.

One fighter, Mr Omar al-Juburi, said they are now backed by soldiers attacking militants in the north of the town, while tribesmen and police fight them in the south.

Ms Jessica Lewis, a former US army intelligence officer who is now research director at the Institute for the Study of War, said holding Dhuluiyah could allow militants to isolate Samarra, a key city to the northwest.

The town could also be used as a staging area for attacks on major military bases, the neutralisation of which would "compromise the strategic defence of Baghdad from the north".

Violence also struck south of Baghdad on Tuesday, with bombings in the Madain area killing nine people, including four soldiers, officials said.

The fighting and bombings came a day after the Pentagon said American military teams sent to Iraq last month had completed their assessment of Iraqi security forces.

The details were not released, but The New York Times said one conclusion was that only roughly half of Iraq's units are capable enough to be advised by US personnel, if the decision is taken to do so.

Though Parliament has finally made progress, deep divisions remain over key appointments and other issues.

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

The Kurdish region's government has laid claim to disputed northern oilfields, having earlier taken control of other contested areas abandoned by Iraqi forces last month as they fled the sweeping offensive led by the jihadist Islamic State group.

Kurdish regional president Massud Barzani has also called for a vote on outright independence.

Mr 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.

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