* Riyadh previously insisted that Shi'ite PM Maliki quit first
* Saudi alarm about ISIL insurgents rises as they near border
* Inclusive Iraq government seen key to quelling rebels
By Lesley Wroughton
SHANNON, Ireland, June 28 (Reuters) - Saudi King Abdullah pledged in talks with U.S. Secretary of State John Kerry to use his influence to encourage Sunni Muslims to join a new, more inclusive Iraqi government to better combat an Islamist insurgency, a senior U.S. official said on Saturday.
After a week of frenetic diplomacy by Kerry tackling the threat of Iraq's disintegration, Abdullah's assurance marked a significant shift from Riyadh's insistence on the removal of Iraqi Prime Minister Nour al-Maliki, a Shi'ite Muslim.
The U.S. official said the Saudi monarch voiced deep concern to Kerry about the Islamic State in Iraq and the Levant (ISIL) insurgents who have overrun much of northern Iraq and its border with Syria and thrust southward, approaching the Saudi frontier.
"It was clear that the two shared a view that all of Iraq's community should be participating on an urgent basis in the political process to allow it to move forward, and that each - both the Secretary and King Abdullah in their conversations with Iraqi leaders - would convey that message directly to them," the U.S. State Department official told reporters after the talks.
Until now Saudi Arabia had been unwilling to support the formation of a new government unless Maliki, accused by critics of a sectarian agenda dedicated to Shi'ite supremacy over Sunnis, stepped aside and does not seek a third term.
U.S.-allied Saudi Arabia, which is the birthplace of Islam and sees itself as a defender of Sunni Muslims in Iraq, has long distrusted Maliki as being too close to Shi'ite Iran.
Last week Saudi officials, in an apparent message to Tehran, warned that foreign countries should stay out of Iraq.
But with Sunni militants now operating close to its border, Saudi Arabia has assured Kerry it will now press Sunni parties to join the new government, appearing more confident that this would undercut Maliki's chances of a third term.
While Washington has not openly called for Maliki to leave, saying it is up to Iraqis to decide who they want as a leader, the United States is also not campaigning for him to stay on.
The Obama administration is now considering air strikes against the insurgents but first wants the new government formed. Baghdad is racing against time as ISIL consolidates its grip on predominantly Sunni provinces in the north and west.
"Both the secretary and the king believe that the security challenge that Iraq faces require a new government," the State Department official said, speaking on condition of anonymity.
"There were no preconditions placed on anything that was discussed with regard to the Iraqi political situation or the situation with the fight against ISIL," the official said, suggesting the Saudis had dropped their demands for Maliki to first leave. "Each of the communities needs to come to the table and put forward candidates for the main positions, and I would say King Abdullah fully agreed," added the official.
NOT INTERFERING in IRAQI POLITICS
King Abdullah, however, made clear that the kingdom "was not in any way interfering inside Iraq's politics."
"That doesn't mean they don't have conversations with - and relationships with - Iraqi political leaders..."
Over the past week Kerry met his counterpart from Turkey while at a NATO meeting in Brussels and in Paris he discussed Iraq and Syria with foreign ministers from Saudi Arabia, Jordan, the United Arab Emirates, Israel and Lebanon.
Maliki, in talks with Kerry in Baghdad this week, said he would meet a July 1 deadline to form a new government that was representative of Iraq and included Sunnis and Kurds.
The senior State Department official was cautious about whether the new government would be formed by then.
"It would be an extremely positive development if we got there. I don't think it's impossible, but it's also Iraq," said the official, noting that "a large number of deadlines for various steps and various political processes, and only a small number that were actually met."
The official reiterated that the United States was not for or against any one candidate.
"As names emerge through the kind of organic Iraqi political process, we're going to be talking to those people. But those are probably people we'd be talking to anyway, because you'd imagine these names are going to be among some prominent political leaders with whom we have relations." (Editing by Sami Aboudi and Mark Heinrich)