Taken together, the statements were the first assertion by the Islamic State group that it had inflicted serious damage on Iraqi military forces engaged in the Ramadi siege.

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BAGHDAD — The Islamic State group broke an uncharacteristic silence Thursday about the Iraqi military’s three-day assault to recapture Ramadi, releasing a flurry of statements asserting that its fighters had killed dozens of Iraqi government forces in attacks in the city and on its outskirts.

In one dispatch released via social media, marked “urgent,” the extremist group said a five-member suicide squad had ambushed police officers at an outpost it identified as the headquarters of the 2nd Regiment of the Federal Police.

Other statements by the group claimed to have killed more than 30 Iraqi soldiers, with suicide bombs and by detonating hidden explosives inside buildings, according to translations of the statements by the SITE Intelligence Group, a research firm in Bethesda, Md., that monitors jihadi postings on the Internet.

Taken together, the statements were the first assertion by the militant group that it had inflicted serious damage on Iraqi military forces engaged in the Ramadi siege.

Those forces began a concerted effort Tuesday to recapture Ramadi, an important city about 60 miles from Baghdad that Islamic State group fighters overran in May in a major humiliation for the central government.

The group’s usual communications avenues had been conspicuously quiet in recent days, other than one site’s release of photographs claiming to show that areas of Ramadi were calm and still under the Islamic State group’s control.

The Islamic State’s loss of Ramadi would be the most significant in a string of recent defeats for the extremist group, which has occupied swaths of Iraq and Syria since last year. Ramadi is the capital of Anbar province, a predominantly Sunni Arab region that has been a stronghold for the militant Sunni group.

Iraqi officials have conceded that their advance in Ramadi has been hampered by hidden explosives and Islamic State group counterattacks, but they denied they had suffered any major casualties Thursday.

Ismael al-Mihlawi, commander of the Anbar government operations room, said that although the Islamic State group had left land mines and booby-traps, “We are moving in the right path, according to our plan. “Ramadi will be liberated soon.”