(Adds Kerry meeting, paragraph 17; Saudi king's order, 18; more U.S. troops arriving, 20)
* Fighting after helicopters land in Tikrit
* Fierce clashes on university campus
* Militants take town north of Baghdad
* Bomb kills eight in Shi'ite district of the capital
* Session of parliament called for July 1
By Oliver Holmes and Isabel Coles
BAGHDAD/ARBIL, June 26 (Reuters) - Iraqi forces launched an airborne assault on rebel-held Tikrit on Thursday with commandos flown into a stadium in helicopters, at least one of which crashed after taking fire from insurgents who have seized northern cities.
Witnesses said battles were raging in the city, hometown of former dictator Saddam Hussein, which fell to Sunni Islamist fighters two weeks ago on the third day of a lightning offensive that has given them control of most majority Sunni regions.
The helicopters were shot at as they flew low over the city and landed in a stadium at the city's university, a security source at the scene said. Government spokesmen did not respond to requests for comment and by evening the assault was still not being reported on state media.
The source, speaking on condition of anonymity, said fierce clashes ensued, centred around the university compound.
Ahmed al-Jubbour, professor at the university's college of agriculture, described fighting in the colleges of agriculture and sports education after three helicopters arrived.
"I saw one of the helicopters land opposite the university with my own eyes and I saw clashes between dozens of militants and government forces," he said.
Jubbour said one helicopter crash-landed in the stadium. Another left after dropping off troops and a third remained on the ground. Army snipers were positioning themselves on tall buildings in the university complex.
Iraq's million-strong army, trained and equipped by the United States, largely evaporated in the north after Sunni fighters led by the Islamic State in Iraq and the Levant launched their assault with the capture of the north's biggest city Mosul on June 10.
But in recent days, government forces have been fighting back, relying on elite commandos flown in by helicopter to defend the country's biggest oil refinery at Baiji.
A successful operation to recapture territory inside Tikrit would deliver the most serious blow yet against an insurgency which for most of the past two weeks has seemed all but unstoppable in the Sunni heartland north and west of Baghdad.
MALIKI UNDER PRESSURE
In the capital, the president's office confirmed that a new parliament elected two months ago would meet on Tuesday, the deadline demanded by the constitution, to begin the process of forming a government.
Prime Minister Nuri al-Maliki, whose Shi'ite-led State of Law coalition won the most seats in the April election but needs allies to form a cabinet, is under strong pressure from the United States and other countries to swiftly build a more inclusive government to undermine support for the insurgency.
Maliki confirmed this week that he would support the constitutional deadlines to set up a new government, after pressure from U.S. Secretary of State John Kerry, who flew to Baghdad for emergency crisis talks to urge him to act.
The 64-year-old Shi'ite Islamist is fighting for his political life in the face of an assault that threatens to dismember his country. Sunni, Kurdish and rival Shi'ite groups have demanded he leave office, and some ruling party members have suggested he could be replaced with a less polarising figure, although close allies say he has no plan to step aside.
Fighters from ISIL - an al Qaeda offshoot which says all Shi'ites are heretics who should be killed - have been assisted in their advance by other, more moderate Sunni armed groups who share their view that Sunnis have been persecuted under Maliki.
Washington hopes that armed Sunni tribal groups, which turned against al Qaeda during the U.S. "surge" offensive of 2006-2007, can again be persuaded to switch sides and back the government, provided that a new cabinet is more inclusive.
Kerry held talks with the foreign ministers of Saudi Arabia, Jordan and the United Arab Emirates on Thursday as part of a diplomatic push on Iraq. He was to travel to Saudi Arabia on Friday for talks with King Abdullah on Iraq and Syria.
In Riyadh, King Abdullah ordered measures to protect his nation against "terrorist threats" after heading a security meeting to discuss the fallout from Iraq, the state news agency said.
The United States, which withdrew its ground forces in 2011, has ruled out sending them back but is despatching up to 300 military advisers, mostly special forces troops, to help organise Baghdad's military response.
The Pentagon said on Thursday that an additional 50 troops had arrived in Baghdad and the first of two Joint Operations Centers had been activated.
The fighters have been halted about an hour's drive north of Baghdad and on its western outskirts, but have pressed on with their advances in areas like religiously mixed Diyala province north of the capital, long one of Iraq's most violent areas.
On Thursday morning, ISIL fighters staged an assault on the town of Mansouriyat al-Jabal, home to inactive gas fields where foreign firms operate, in northeastern Diyala province. An Iraqi oil ministry official denied fighters had taken the field.
A roadside bomb in Baghdad's Shi'ite northern district of Kadhimiya killed eight people on Thursday, police and hospital sources said.
The ISIL-led advance has put the United States on the same side as its enemy of 35 years Iran, the Middle East's main Shi'ite power, as well as Iran's ally President Bashar al-Assad of Syria, who is fighting ISIL in his country.
Locals in the Iraqi border town of al-Qaim, captured by ISIL several days ago, say Syrian jets carried out strikes against militants on the Iraqi side of the frontier this week, marking the first time Assad's air force has come to Baghdad's aid.
Publicly, Baghdad, which operates helicopters but no jets, said its own forces carried out the air strike. But a senior Iraqi government official confirmed on condition of anonymity that the strike was mounted by the Syrian air force.
Iran, which armed and trained some of Iraq's Shi'ite militias, has pledged to intervene in Iraq if necessary to protect Shi'ite holy places. Thousands of Shi'ites have answered Maliki's call to join the armed forces to defend the country.
British Foreign Secretary William Hague arrived in Baghdad on Thursday, reinforcing the international push for Maliki to speed up the political process.
Under the official schedule, parliament will have 30 days from when it first meets on Tuesday to name a president and 15 days after that to name a prime minister.
In the past the process has dragged out, taking nine months to seat the government in 2010. Any delays would allow Maliki to continue to serve as caretaker. (Additional reporting by Isra' al-Rubei'i in Baghdad, Phil Stewart in Washington, Lesley Wroughton in Paris, Sami Aboudi in Dubai and Sylvia Westall in Beirut; Editing by Peter Graff and Mohammad Zargham)