* Blast hits contested ethnically mixed city of Kirkuk
* Attack follows suicide bomb attack on Sunni lawmaker
* Kurds locked in dispute with Baghdad government
By Mustafa Mahmoud
KIRKUK, Iraq, Jan 16 (Reuters) - More than 35 people died in a suicide attack and other bombings in northern Iraq and Baghdad on Wednesday, worsening sectarian strife as Prime Minister Nuri al-Maliki faces mounting pressure from minority Sunni Muslims and Kurds.
Shoppers and police helped drag bloodied survivors out of the rubble and wrecked vehicles after a car bomb and a suicide bomber in a truck set off huge blasts in Kirkuk, near the local headquarters of the Kurdistan Democratic Party (KDP).
Maliki, a Shi'ite Muslim, is locked in a feud with ethnic Kurds in autonomous Iraqi Kurdistan over disputed oilfields and is also confronting Sunni protesters in a western province calling for him to step down.
"A suicide bomber driving a truck packed with explosives detonated the vehicle outside the KDP headquarters. It's a crowded area; dozens were killed and wounded," Police Brigadier Sarhat Qadir told Reuters in Kirkuk.
Local Kirkuk health officials and police said at least 25 people were killed and more than 180 were wounded.
Another five people died and 37 more were wounded in another bombing outside a rival Kurdish political party office in Tuz Khurmato, 170 km (105 miles) north of Baghdad.
Roadside bombs and gun attacks in Baghdad and Baiji, north of the capital, killed seven policemen and soldiers.
A year after the last U.S. troops left, Iraq's government of Sunni, Shi'ite and Kurdish parties is mired in a crisis over how to share power, increasing worries that the OPEC member state may relapse into wide-scale sectarian bloodshed
Violence and unrest are compounding concern that the conflict in neighbouring Syria, where mainly Sunni rebels are fighting Shi'ite Iran's ally President Bashar al-Assad, will upset Iraq's own delicate sectarian and ethnic balance.
Wednesday's attacks came a day after a suicide bomber killed an influential Sunni Muslim lawmaker in the west of Iraq, where thousands of Sunni protesters have been holding mass demonstrations against Maliki.
Sunni turmoil erupted in late December after state officials arrested members of a Sunni finance minister's security team on terrorism charges. Authorities denied the arrests were political, but Sunni leaders saw them as a crackdown.
Since the fall of Sunni strongman Saddam Hussein after the 2003 U.S.-led invasion, many Sunnis feel they have been marginalised by the leadership of the Shi'ite majority.
Maliki's National Alliance Shi'ite coalition and Sunni-backed Iraqiya bloc held preliminary talks in parliament on Wednesday in attempt to defuse the crisis by addressing the demands of the demonstrations.
"We have to admit that we have a tough job ahead to reach common ground," Ali al-Shallah, a lawmaker with Maliki's alliance. "All the blocs agree to allow time for the government to review protest demands; that's one step."
Deputy Prime Minister Hussein al-Shahristani, a prominent Shi'ite who heads the committee investigating protest demands, said the government had so far freed more 400 detainees held under anti-terrorism laws as a concession.
But protesters want detainees released, a modification of terrorism laws and more control over a campaign against former members of Saddam's outlawed Baath party, a measure they believe is being used unfairly to sideline their leaders.
Violence in Iraq is down since the height of sectarian bloodletting in 2006-2007, when thousands were killed. But last year witnessed a rise in deaths for the first time in three years with more than 4,400 people killed in attacks.