BAGHDAD (Reuters) - Bombings on Shi'ite neighborhoods in Baghdad and a blast on an Iranian pilgrim bus killed more than 30 people on Saturday, marring Iraqi celebrations of the second day of the Islamic Eid al Adha religious festival.

Violence in Iraq has eased sharply, but Sunni Islamist insurgents and al Qaeda's Iraq wing often target Shi'ites in an attempt to stir up the kind of sectarian tensions that dragged the country close to civil war in 2006-2007.

Two car bombs exploded on Saturday, one ripping into a restaurant in the Shi'ite stronghold of Sadr City and killing at least 23 people, police and hospital sources said.

"I was just selling fruit and we were surprised by a huge explosion on the other side of the street," Hassan Falih Shami, a grocery stall owner near the site of the blast. "You can see pools of blood, the shoes and pieces of clothing."

Hours earlier, a roadside bomb planted near an open-air market killed seven people, including three children at a playground. Another blast killed six people when it hit a bus carrying Iranian pilgrims to a Baghdad shrine, police and hospital officials said.

Police said the attack on the Iranian pilgrims came from a bomb that had been attached to their bus. It exploded around 300 meters (yards) from a police checkpoint, sending the bus out of control before it flipped over on its side.

Insurgents have carried out at least one major attack a month since the last U.S. troops left in December. Iraqi officials worry Syria's crisis is bolstering Iraqi insurgents.

The monthly death toll from attacks in Iraq doubled in September to 365, the highest number of casualties in two years, including a series of bombings targeting Shi'ite neighborhoods that killed more than 100 people.

Security officials had said they believe insurgents would try to carry out a large attack during the religious holiday, which started on Friday.

Car bombs exploded and mortars landed around the Shi'ite neighborhood of Shula, northwestern Baghdad, on Tuesday killing eight people and wounded 28, and another person was killed by a mortar round in Kadhimiya area.

(Reporting by Raheem Salman; Writing by Patrick Markey; Editing by Jon Hemming)