* Al Qaeda accused of orchestrating the attacks
* Violence last year the worst since 2006-07 peak
* Sunnis feel sidelined since majority Shi'ite rule began in 2003 (Adds Sadr speech)
By Ahmed Rasheed and Ali al-Rubaie
BAGHDAD/HILLA, Iraq, Feb 18 (Reuters) - Bombs exploded in predominantly Shi'ite Muslim districts of the Iraqi capital and in the southern city of Hilla on Tuesday, killing at least 49 people, police and hospital sources said.
No group immediately claimed responsibility for any of the attacks, but Shi'ites are a target for Sunni Islamist insurgents who have been regaining ground in Iraq over the past year and overran several towns in recent weeks.
Hilla police chief, Major General Abbas Abid, blamed groups linked to al Qaeda.
"Al Qaeda terrorist groups stand behind today's attacks in Hilla to confuse the security forces and cause high casualties among civilians," he said. "They are criminals and they never get enough of innocent blood".
Prime Minister Nuri al-Maliki has appealed for international support and weapons to fight Sunni Islamist al Qaeda, 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 minority deeply resent Maliki and feel they have been sidelined in the Shi'ite-led political order that took shape following the U.S.-led invasion in 2003.
Some fellow Shi'ites also accuse Maliki of abusing his power. Powerful Shi'ite Muslim cleric Moqtada al-Sadr, who withdrew from politics at the weekend, said Iraq was governed by "wolves thirsty for blood and money".
"Politics has become a door for injustice and recklessness, despotism and abuse, so that a dictator and tyrant can take over and seize control in order to plunder money, break necks, fight cities and divide sects."
Sadr, who led revolts against U.S. forces in Iraq before their pullout and went on to become a major influence in the government, said he had decided to retire in order to distance himself from a "failed, corrupt and unjust government".
"Whenever a Shi'ite, Sunni or Kurd objects to them, they accuse him of sectarianism or being a terrorist".
CAR BOMB EXPLOSIONS
In Tuesday's attacks, 35 people were killed in seven car bomb explosions inside Hilla, 100 km (60 miles) south of Baghdad, and the nearby towns of Haswa, Mahaweel and Mussayab. At least 90 people were wounded.
"I was sitting in my shop when suddenly a powerful blast smashed the front window," said Ali Mousa, whose mini-market was near the site of one bomb in central Hilla. "I went out to see what happened and saw bodies on the ground and wounded people bleeding and shouting for help".
Fourteen people were killed in explosions in mainly Shi'ite districts of Baghdad. In one, a bomb inside a parked vehicle exploded near a bus station in the Bayaa district, killing five people, the sources said. There were also blasts in the Amil, Ilam and Shurta districts.
Last year was Iraq's bloodiest since sectarian violence began to abate in 2008.
The city of Falluja in Iraq's Sunni-dominated province of Anbar has been under siege by the army since early January, when militants overran it after security forces cleared a site where Sunnis were protesting against Maliki.
In northern Iraq, troops are fighting to wrest control of Sulaiman Pek from Sunni militants who took over parts of the town last Thursday and raised the black flag of the Islamic state in Iraq and the Levant (ISIL) over it.
ISIL is active in neighbouring Syria and seeks to establish a Sunni state spanning the border into Iraq. The group also has a presence in the city of Falluja, along with other Sunni militants and anti-government fighters.
Deteriorating security in Anbar has raised doubts that parliamentary elections can be held nationwide in April as planned. Sadr encouraged people to vote but said he himself would not take part or back any side.
"All should widely participate in election in order not to let the government fall into untrustworthy and malicious hands". (Additional reporting by Kareem Raheem in Baghdad; Writing by Isabel Coles; Editing by Jon Boyle and Sonya Hepinstall)