By Aref Mohammed

BASRA, Iraq (Reuters) - Attacks across Iraq targeting mainly Shi'ite Muslims killed at least 30 people on Sunday, police and medics said, intensifying fears of a descent into all-out sectarian war.

Ten years after the U.S.-led invasion that toppled Sunni leader Saddam Hussein, a stable power-sharing compromise between Iraq's Sunni, Shi'ite and ethnic Kurdish factions is still elusive and violence is on the rise.

More than 1,000 people were killed in militant attacks in May, according to the United Nations, making it Iraq's deadliest month since the intercommunal strife of 2006-07.

Regional sectarian tensions have been inflamed by the conflict in Syria, Iraq's neighbor, where Sunni rebels are fighting to overthrow a leader backed by Shi'ite Iran.

Two car bombs exploded minutes apart in the predominantly Shi'ite southern oil hub of Basra, 420 km (260 miles) southeast of Baghdad, killing at least five people and tearing off shop fronts.

"We heard a bang and rushed outside," said Ali Fadhil, who was working at a nearby bakery. "I saw cars on fire, dead bodies covered with blood, and wounded people lying on the ground screaming for help."

"When police arrived, a second blast struck which was more powerful, leaving the street in a state of total destruction."

Another car bomb exploded in a busy market in the Shi'ite holy city of Najaf, killing at least seven people, and blasts also targeted Shi'ites in Nassiriya, Kut, Hilla, Tuz Khurmato and Mahmudiya in southern Baghdad.

Near the northern city of Mosul, gunmen shot dead six policemen at a checkpoint in Hadhar, police said.

No group claimed responsibility for the attacks but Sunni Islamist insurgents and al Qaeda's Iraqi wing have increased their activities this year, seeking to provoke wider confrontation between Sunnis and Shi'ites.

Sunnis in Iraq resent Shi'ite domination since 2003 and have been crossing into Syria to fight against President Bashar al-Assad. Iraqi Shi'ite militia and Lebanese Hezbollah guerillas have also joined the war on Assad's side.

(Additional reporting by Kareem Raheem, Mustafa Mahmoud, Ali al-Rubaie, Ziad al-Sanjary, Suadad al-Salhy and Ahmed Rasheed; Writing by Isabel Coles; Editing by Louise Ireland)