* Bombings marked deadliest Ramadan in years
* Merged Iraq-Syria al Qaeda group claims attack
* Bomb explodes near school northeast of Baghdad (Adds more al Qaeda quotes, attack)
By Sylvia Westall
BAGHDAD, Aug 12 (Reuters) - Al Qaeda claimed responsibility for a series of bombings in Iraq which killed dozens of people during a Muslim holiday and warned the government to stop arresting suspected militants or face more violence.
The Islamic State of Iraq and the Levant (ISIL), formed earlier this year through a merger of al Qaeda's affiliates in Syria and Iraq, said on jihadist forums it was behind the attacks across Baghdad and southern provinces on Saturday.
"The Islamic State deployed some of its security efforts in Baghdad and the southern province and other places to deliver a quick message," ISIL said, according to the SITE Monitoring group, which tracks jihadist websites.
Bombs ripped through markets, shopping streets and parks late on Saturday as Iraqi families were out celebrating Eid al-Fitr, the end of the Muslim fasting month of Ramadan. Nearly 80 people were killed and scores wounded, police and medical sources said.
On Monday, there was no respite from the violence. A roadside bomb close to a school killed two people and wounded 11, including children, in the town of Muqdadiya, 80 km (50 miles) northeast of Baghdad, police said. It was not immediately clear who was behind the attack.
It has been one of the deadliest Ramadan holidays in years in Iraq, where Sunni Islamist militants are waging an insurgency against the Shi'ite-led government.
July had the highest monthly death toll from attacks since 2008, with more than 1,000 Iraqis killed, according to United Nations statistics.
The renewed violence prompted a statement from Washington condemning the attacks and offering to work closely with Baghdad to confront al Qaeda and other groups.
ISIL, which has also claimed responsibility for jail breaks in Iraq last month in which hundreds of convicts escaped, said a government campaign to arrest suspects and ramp up security in the capital had only made things worse.
"They will pay a high price for what they did, and they will not be secure day or night during Eid or other times," the ISIL statement said according to the SITE translation.
"They should watch their footsteps and stop the detention campaigns and cease harming the Sunni clans, and ... expect more of what will harm them and what will bring them to their senses."
The Interior Ministry, which said last month it was facing an "open war", said on Sunday that media reports about the attacks had been exaggerated and that its recent security crackdown had been effective. (Editing by Elizabeth Piper)