* Blasts occur near Ministry of Foreign Affairs
* Sunni Islamist militants regaining ground in Iraq
* Critics say PM Maliki's policies have fostered insurgency (Updates death toll)
By Kareem Raheem
BAGHDAD, Feb 5 (Reuters) - A spate of bombings in Baghdad killed at least 34 people on Wednesday, including several blasts near the heavily-fortified "Green Zone" and a busy square in the centre of the capital, Iraqi security sources said.
The blasts came a day after two rockets were fired into the Green Zone, home to the prime minister's office and Western embassies, and are likely to heighten concerns about Iraq's ability to protect strategic sites as security deteriorates.
No group immediately claimed responsibility for the bombings, but Sunni Islamist militants have been regaining ground in Iraq, particularly in the western province of Anbar, where they overran two cities on Jan. 1.
More than 1,000 people were killed in violence across the country in January alone, and last year was the bloodiest since 2008, when sectarian warfare began to abate from its height.
On Wednesday, security sources said two parked car bombs went off opposite the Ministry of Foreign Affairs, killing 11.
The Interior Ministry gave a different version, blaming the "cowardly" attack on a suicide bomber on a motorcycle.
"At around nine o'clock this morning, a terrorist suicide bomber riding a motorcycle tried to enter the security area of the Ministry," it said in a statement. "A group of guards stopped him at a checkpoint and denied him access so he blew himself and the bike up."
In a separate incident, a suicide bomber driving a car detonated himself along with the vehicle outside a restaurant close to a checkpoint one street away from the Green Zone, killing eight people, the security sources said.
An explosion near Khullani Square in central Baghdad left four more people dead, and later in the day, three car bombs blew up in quick succession in the southeastern Jisr Diyala district, killing a further 11.
"Iraqi political leaders should show national unity in dealing with such threats and unite against terrorism," said the U.N. envoy to Iraq, Nikolay Mladenov, in a statement.
The city of Falluja is currently being surrounded and shelled by the Iraqi army in preparation for a possible ground assault to drive out anti-government fighters, which include members of the Islamic State in Iraq and the Levant (ISIL).
The violence has halted exports of crude oil from Iraq to Jordan, which used to be trucked across the border through Anbar.
In a short speech broadcast on state television on Wednesday, Prime Minister Nuri al-Maliki said local authorities and tribal leaders in Anbar would unveil a joint initiative to end the standoff in the coming days, without elaborating.
"The goal of this initiative is to unify positions to end the battle against al Qaeda," said Maliki, who is also commander in chief of the armed forces. "The battle is on the threshold of conclusion."
Maliki has appealed for international support and weapons to fight al Qaeda, but critics say his own policies towards Iraq's once-dominant Sunni community are at least partly to blame for reviving an insurgency that had peaked in 2006-07.
Some tribes in Sunni-dominated Anbar support or have aligned themselves with ISIL against Maliki's Shi'ite-led government, which they accuse of abuses against their sect.
Others deplore ISIL's violent tactics and have joined forces with the army to fight against the group and its allies in and around the city of Ramadi, which was also overrun by militants last month but is now largely back under government control.
New York-based Human Rights Watch (HRW) said ISIL's acts of violence amounted to crimes against humanity, citing the recent execution-style killing of four members of Iraq's SWAT forces near Ramadi, for which the militants claimed responsibility.
"These abhorrent killings are the latest in a long list of ISIL atrocities, at a time when civilians in Anbar province are stuck in the fighting and getting abused by all sides," said HRW's deputy Middle East director Joe Stork on Wednesday.
"Together with the ISIL car bombs and suicide attacks targeting civilians, they are further evidence of crimes against humanity." (Additional reporting by Raheem Salman and Ahmed Rasheed; Writing by Isabel Coles; Editing by Gareth Jones)