* Seven civilians killed in army push to repel militants from Muqdadiya base
* Death toll rises to 30 in suicide attack in Kirkuk province
* Second session of parliament now set for Sunday
* PM Maliki's opponents accuse him of divisive rule (Adds deaths in Falluja, Jalawla, context of sectarian killings)
By Ahmed Rasheed and Maggie Fick
BAGHDAD, July 12 (Reuters) - Iraqi soldiers backed by Shi'ite militias fought Sunni rebels for control of a military base northeast of Baghdad on Saturday as a U.N. envoy warned of chaos if divided lawmakers do not make progress on Sunday towards naming a government.
Forces loyal to Prime Minister Nuri al-Maliki launched an early morning push to repel Islamic State militants who fought their way on Thursday into a military base on the edge of Muqdadiya, 80 km (50 miles) northeast of the capital.
Heavy fighting raged for hours and was continuing on Saturday afternoon, local security sources said.
Sources at the morgue and hospital in the nearby town of Baquba said they had received the bodies of 15 Shi'ite militia fighters transferred after the morning's fighting. State TV also reported that 24 "terrorists" had been killed. Seven civilians including children from nearby villages were killed by helicopter gunship fire, police and medics said.
The Sunni militants had moved toward the base after seizing the town of Sadur just to the north, another security source and eyewitnesses said. They were equipped with artillery and mortars and drove vehicles including captured tanks and Humvees.
In the western city of Falluja, a hospital received three bodies and 18 wounded people on Saturday after army helicopters bombed the city, government health official Ahmed al-Shami said.
Kurdish peshmerga security forces attacked Islamic State positions in Jalawla late Friday night, killing at least 15 militants and three Kurdish security personnel, spokesman Halgurd Hikmat said. The town, in the eastern province of Diyala near the Iranian border, was seized by insurgents last month.
Bickering lawmakers in Baghdad are under pressure from the United States, the United Nations and Iraq's own Shi'ite clerics to form a new government swiftly to deal with the Sunni insurgency, which seized territory in the north and west last month, and has held it in the face of ground and air attacks.
Few doubt that an inclusive government is needed to hold Iraq together, but there is no consensus on who should lead it.
The national parliament elected in April met for the first time on July 1 but failed to agree on nominations for the top three government posts.
The U.N. special envoy to Iraq, Nickolay Mladenov, said the country could plunge into chaos if parliament fails to move forward on a government in a next session now set for Sunday.
He also urged lawmakers to turn up, after fewer than a third attended the first session when Sunnis and Kurds walked out after Shi'ites failed to nominate a premier to replace Maliki.
MALIKI SITTING TIGHT
Most of Iraq's Sunnis and Kurds demand Maliki leave office, and Shi'ites are divided, but he shows no sign of quitting.
Under a system created after the removal of Saddam Hussein in 2003, the prime minister has always been a member of the Shi'ite majority, the speaker of parliament a Sunni and, with one exception, the occupant of the largely ceremonial presidency has been a Kurd.
With politics in Baghdad paralysed, and Maliki continuing in a caretaker role, the fighting rages on.
The death toll rose to 30 on Saturday from a suicide bomb attack on Friday at a Kurdish-controlled checkpoint on the southern edge of Kirkuk province, where families fleeing violence in Tikrit and other areas overrun by militants last month were waiting to pass through.
Maliki's opponents accuse him of ruling for the Shi'ite majority at the expense of the Sunni and Kurdish minorities, and want him to step aside.
Senior Shi'ite parliamentarian Bayan Jaber, a former interior and finance minister, said on Thursday that he hoped the Shi'ite National Alliance bloc, in which Maliki's State of Law coalition is the biggest group, could agree on its nominee for prime minister before Sunday's meeting.
But he said that if Maliki remained the sole nominee, "the problem will remain".
Prominent Sunni Arab lawmaker Dhafer al-Ani said this week that "partition of Iraq will be the natural result" if the Shi'ite bloc could not put forward another candidate.
"If they insist on Maliki as the prime minister, then we will withdraw from the government," he said. "I believe that it would be hard for any Sunni politician to raise his hand and vote for Maliki as prime minister for a third term."
The head of the Kurdish Gorran bloc, Aram Sheikh Mohammed, said Kurdish factions would attend Sunday's session, but the prospects of progress were poor.
"If Maliki nominates himself, I think neither the Sunnis nor Kurds will nominate their candidates (for speaker and president)," he said.
Kurdish forces seized two oilfields in northern Iraq from a state-run oil company on Friday.
The political deadlock raises fears that Iraq could splinter along ethnic and sectarian lines, a reality already playing out in parts of the country.
Iraq's top Shi'ite cleric, Grand Ayatollah Ali Sistani, urged fighters on Friday to respect the rights of all Iraqis, regardless of sect or politics.
There have been many reports of disappearances and suspected mass killings since the insurgents' offensive began last month.
A prominent man in the Sunni majority town of Buhriz, 35 miles northeast of Baghdad was kidnapped from his home on Friday night and found dead hours later, police said.
Tensions are high in Sunni areas north of Baghdad where Islamic State militants have lashed out at communities they see as supporting government forces.
Iraqi security forces and government affiliated militias appear to have unlawfully executed at least 255 prisoners over the past month in apparent revenge for killings by Islamic State fighters, a Human Rights Watch report said.
(Additional reporting by Raheem Salman, Dominic Evans and Reuters TV in Baghdad, Kamal Namaa in Ramadi, and Isabel Coles in Arbil; Writing by Maggie Fick; Editing by Kevin Liffey and David Evans)