* Islamic State fighters edge closer to Kurdish region
* Kurds fight back after suffering weekend defeat
* Kurdish official says Yazidi minority needs urgent help (Adds quotes, details)
By Ahmed Rasheed and Isra' al-Rubei'i
BAGHDAD, Aug 6 (Reuters) - Kurdish forces attacked Islamic State fighters on Wednesday just 40 kilometers (25 miles) southwest of the Kurdish regional capital of Arbil in northern Iraq, a senior Kurdish official told Reuters.
The attack came after Islamic State militants inflicted a humiliating defeat on the Kurds on Sunday with a rapid advance through three towns, prompting Iraq's prime minister to order his air force for the first time to back the Kurdish forces.
"We have changed our tactics from being defensive to being offensive. Now we are clashing with the Islamic State in Makhmur," said Jabbar Yawar, secretary-general of the ministry of the Kurdish peshmerga fighters.
The location of the clashes puts the Islamic State militants closer than they have ever been to the Kurdish semi-autonomous region since they swept through northern Iraq almost unopposed in June.
Shortly after that lightning advance, thousands of U.S.-trained Iraqi soldiers fled. Kurdish fighters, who often boast of their battles with Saddam Hussein's forces, stepped in as did Iranian-trained Shi'ite militias.
Yawar said the Kurds had re-established military cooperation with Baghdad. Ties had been strained between the Kurdish leadership and the Shi'ite-led government of Prime Minister Nuri al-Maliki over oil, budgets and land.
But the dramatic weekend offensive by the Sunni militants - who seized more towns, a fifth oilfield and Iraq's biggest dam - prompted them to bury their differences.
YAZIDI MINORITY AT RISK
"The peshmerga ministry sent a message to the Iraqi defence ministry requesting the convening of an urgent meeting on military cooperation. The joint committees have been reactivated," said Yawar by telephone.
The Islamic State, which has declared a 'caliphate' in swathes of Iraq and Syria that it controls and threatens to march on Baghdad, poses the biggest threat to OPEC member Iraq since a U.S.-led invasion toppled Saddam in 2003.
Islamic State fighters and their Sunni militant and tribal allies also hold parts of western Iraq.
Efforts to neutralise the Islamic State have been undermined by political deadlock and sectarian tensions fueling levels of violence not seen since the height of a civil war in 2006-2007.
Critics say Maliki is an authoritarian leader whose sectarian agenda has sidelined Sunnis and driven them to find common cause with the Islamic State, even though they reject the group's radical view of Islam.
Maliki, who has been serving in a caretaker capacity since an inconclusive election in April, has rejected calls by Kurds, Sunnis, some fellow Shi'ites and even regional power-broker Iran to step aside and make room for a less polarising figure.
He remained defiant on Wednesday in his weekly televised address to the nation, warning any unconstitutional attempt to form a new government would open "the gates of hell" in Iraq.
Maliki rejected any outside interference in the process, an apparent reference to Tehran, which Iranian officials have said believes Maliki can no longer hold Iraq together.
Iran is now backing calls by Iraq's top cleric Grand Ayatollah Ali al-Sistani for Maliki to go and is looking for an alternative leader to combat the Sunni Islamist insurgency, said the Iranian officials.
The United States, which was a key backer of Maliki when he fist came to office as an unknown in 2006, has urged Iraqi politicians to form a more inclusive government that can unify Iraqis and take on the Islamic State.
The Islamic State, which believes Iraq's majority Shi'ites are infidels who deserve to be killed, has put Iraq's survival as a unified state in jeopardy.
It seized three more towns and a fifth oilfield and reached Iraq's biggest dam during the weekend offensive.
The capture of one of the towns, Sinjar, home to many of Iraq's Yazidi minority sect, could lead to a humanitarian crisis.
Yazidis, who are ethnic Kurds and followers of an ancient religion derived from Zoroastrianism, are at high risk of being executed because they are viewed by the Islamic State Sunni militants as devil worshippers.
Yawar said 50,000 Yazidis now hiding on a mountain risked starving to death if they were not rescued within 24 hours.
"Urgent international action is needed to save them. Many of them, mainly the elderly, children and pregnant women, have (already) died," he said.
"We can't stop the Islamic State from attacking the people on the mountain because there is one paved road leading up to the mountain and it can be used by them. They (Islamic State) are trying to get to that road."
There are no signs that the revived military cooperation between the Kurdish Regional Government and the Baghdad government has eased the dangers posed by the Islamic State.
State television reported that Kurdish forces backed by Maliki's air force launched a surprise attack on the city of Mosul, a major urban centre held by the Sunni militants.
Scores of Islamic State fighters fled, said state television.
Witnesses told Reuters there was no major attack, just hit-and-run attacks by both sides and exchange of mortar fire over the past few days which has damaged residential areas.
People in nearby Bashiqa, a diverse town with churches, mosques and Yazidi temple, were taking no chances. Its inhabitants fled, a source at a non-profit organisation in the town said by telephone.
(Additional reporting by David Sheppard in London; Writing by Michael Georgy, editing by Peter Millership)