BAGHDAD (Reuters) - At least 20 people were killed in Iraq when three mortar rounds struck a crowded market in a mainly Shi'ite Muslim town of Mussayab on Thursday evening, police and medics said.

It was not clear who fired the mortars or from where, but the Shi'ite community is a target of Sunni Islamist insurgents who have been regaining ground in Iraq over the past year and in recent weeks overran several towns.

The attack on Mussayab, 60 km (40 miles) south of the capital Baghdad, also wounded 35 people. Police said the death toll was high because the market is usually crowded with shoppers in the evening when the attack took place.

Last year was Iraq's bloodiest since sectarian violence began to abate in 2008.

Iraqi Prime Minister Nuri al-Maliki says the upsurge is a spillover from the civil war in neighboring Syria but critics say his own policies are at least partly to blame for reviving an insurgency that climaxed in 2006-07.

Many in Iraq's once-dominant Sunni Muslim minority feel they have been sidelined in the Shi'ite-led political order that took shape after the U.S.-led invasion in 2003 that toppled Sunni dictator Saddam Hussein.

(Reporting by Ali al-Rubaie; Writing by Isabel Coles; Editing by Mark heinrich)