* Seven people from same family killed

* Attacks underline sectarian, ethnic tensions

* Thousands of Sunnis have protested against Shi'ite PM (Updates death toll, adds detail, analyst comment)

BAGHDAD, Dec 31 (Reuters) - Explosions killed at least 16 people and wounded 76 across Iraq on Monday, police said, underlining sectarian and ethnic divisions that threaten to further destabilise the country a year after U.S. troops left.

Tensions between Shi'ite, Kurdish and Sunni factions in Iraq's power-sharing government have been on the rise this year. Militants strike almost daily and have staged at least one big attack a month.

The latest violence followed more than a week of protests against Shi'ite Prime Minister Nuri al-Maliki by thousands of people from the minority Sunni community.

No group claimed responsibility for any of Monday's attacks, which targeted government officials, police patrols and members of both the Sunni and Shi'ite sects.

Seven people from the same Sunni family were killed by a bomb planted near their home in the town of Mussayab, south of Baghdad.

In the Shi'ite majority city of Hilla, also in the south, a parked car bomb went off near the convoy of the governor of Babil province, missing him but killing two other people, police said.

"We heard the sound of a big explosion and the windows of our office shattered. We immediately lay on the ground," said 28-year-old Mohammed Ahmed, who works at a hospital near the site of the explosion.

"After a few minutes I stood up and went to the windows to see what happened. I saw flames and people lying on the ground."

In the capital Baghdad, five people were killed by a parked car bomb targeting pilgrims before a Shi'ite religious rite this week, police and hospital sources said.

Although violence is far lower than during the sectarian slaughter of 2006-2007, about 2,000 people have been killed in Iraq this year following the withdrawal last December of U.S. troops, who led an invasion in 2003 to overthrow Sunni dictator Saddam Hussein.

SUNNIS PROTEST

Monday's violence also included a series of blasts that killed three people in Iraq's disputed territories, over which both the central government and the autonomous Kurdish region claim jurisdiction.

Two of those deaths were in the oil-producing, ethnically mixed city of Kirkuk, where a bomb exploded as a police team tried to defuse it.

Baghdad and Kurdistan are locked in a feud over land and oil rights and recently deployed their respective armies to the swathe of territory along their contested internal boundary, where they are currently facing off against one other.

Efforts to ease the standoff stalled when President Jalal Talabani, a Kurd seen as a steadying influence, suffered a stroke and was flown abroad for medical care in December.

Maliki then detained the bodyguards of his Sunni finance minister, which ignited anti-government protests in the western province of Anbar, a Sunni stronghold on the border with Syria.

A lecturer in law at Baghdad University said the protests could help create the conditions for militant Islamist groups like al Qaeda to thrive. 

"Raising tension in Anbar and other provinces with mainly Sunni populations is definitely playing into the hands of al Qaeda and other insurgent groups," Ahmed Younis said.

More than 1,000 people protested in the city of Samarra on Monday and rallies continued in Ramadi, centre of the protests, and in Mosul, where about 500 people took to the streets.

Protesters are demanding an end to what they see as the marginalisation of Sunnis, who dominated the country until the U.S.-led invasion. They want Maliki to abolish anti-terrorism laws they say are used to persecute them.

On Sunday, Deputy Prime Minister Saleh al-Mutlaq, himself a Sunni, was forced to flee a protest in Ramadi when demonstrators pelted him with stones and bottles.

The civil war in neighbouring Syria, where majority Sunnis are fighting to topple a ruler backed by Shi'ite Iran, is also whipping up sectarian sentiment in Iraq.

"The toppling of President Bashar al-Assad and empowerment of Sunnis (in Syria) will definitely encourage al Qaeda to regain ground," Younis said. (Reporting by Ali al-Rubaie in Hilla, Mustafa Mahmoud and Omar Mohammed in Kirkuk, Ali Mohammed in Baquba and Ahmed Rasheed and Aseel Kami in Baghdad; Writing by Isabel Coles; Editing by Angus MacSwan)