(Adds comment from Hagel)
By Lesley Wroughton and Jane Wardell
SYDNEY, Aug 11 (Reuters) - U.S. Secretary of State John Kerry said on Monday the formation of an Iraqi government was critical for stability and urged Prime Minister Nuri al-Maliki not to stoke political tension further.
U.S. President Barack Obama has urged Iraqi political leaders to bury their sectarian differences and form a more inclusive government that can unite Iraqis against Islamic State militants.
The United States has carried out three consecutive days of air strikes over Iraq, stepping up assistance to Kurdish forces to counter the advance of the militants in the north of the country.
Amid the violence, political pressure is mounting as special forces loyal to Maliki deployed in strategic areas of Baghdad on Sunday night after he delivered a tough speech indicating he would not cave in to pressure to drop a bid for a third term.
"The government formation process is critical in terms of sustaining stability and calm in Iraq, and our hope is that Mr Maliki will not stir those waters," Kerry told reporters in Sydney ahead of annual Australia-United States Ministerial Consultations (AUSMIN).
"One thing all Iraqis need to know, that there will be little international support of any kind whatsoever for anything that deviates from the legitimate constitution process that is in place and being worked on now."
At a separate briefing in Sydney, Defense Secretary Chuck Hagel said that the air strikes "have been very effective from all of the reports we've received on the ground".
"We're constantly assessing where we can continue to assist the Iraqi security forces and where as we build partnerships we will work with the Iraqi government," Hagel said.
Kerry said it was up to Iraqis to decide who their prime minister was going to be, but added it was clear civilians were looking for change.
Maliki, who has been premier since 2006, has alienated some allies, including the United States, who blame him for failing to forge consensus and fuelling sectarian violence that is breaking Iraq apart.
A bloc comprising Iraq's biggest Shi'ite parties is close to nominating a prime minister, the deputy speaker of parliament Haider al-Abadi said in a tweet on Monday, directly challenging Maliki.
"What we urge the people of Iraq to do is to be calm, there should be no use of force, no introduction of troops or militias in this moment of democracy for Iraq," Kerry said.
Australia, along with France and Britain, has offered assistance to provide aid to thousands of Iraqi citizens trapped by Islamic militants in the northern Sinjar mountains. U.S. officials said on Sunday they were exploring options to evacuate the group, made up of the Yazidi minority, following air drops of food and water.
"We are coordinating a group of partners to assist in this effort," Hagel told reporters, noting that Obama had spoken to French President Francois Hollande and British Prime Minister David Cameron, who had both offered assistance.
"This is a humanitarian issue of great consequence for all of the world and I think great powers understand they have responsibility in these areas," Hagel said. "It's well underway, those last details of planning and we'll have more to announce."
Asked whether the United States was prepared to allow the self-styled Islamic State to remain in places it has already occupied or make an effort to push them out, Hagel said:
"President Obama has made it very clear, ISIL is a threat to the civilised world, certainly to the United States, to our interests, it is to Europe, it is to Australia," Hagel said. "As to how the United States is responding to that threat in Iraq, the president has also made it clear, we're going to continue to support the Iraqi forces in every way we can."
Hagel later said the Middle East was as "unpredictable, dangerous, complicated" as it had ever been.
"This is again why a military solution is not going to end it or fix it," he said in an interview with Australia's ABC.
"If we don't all assist in some ways, not to impose, not to dictate, not to get in the middle of it, but help facilitate these political settlements, then the Middle East will continue to get worse." (Editing by Jeremy Laurence and Clarence Fernandez)