DHAKA, Bangladesh — The Islamic State has claimed responsibility for the shooting death of an Italian aid worker in this city’s diplomatic quarter. If the claim is verified, the killing on Monday night will have been the Islamic State’s first attack in Bangladesh, a country that has been grappling this year with a series of attacks on bloggers who have written critically of Islam.

The aid worker, Cesare Tavella, 50, was shot about 6:15 p.m. as he was jogging. The police said he appeared to have been ambushed by three men who had pulled to the side of the road on a motorcycle. The men fired at Mr. Tavella at least three times before fleeing on the bike.

“We think it was a preplanned killing,” said Mohammad Abdul Ahad, a police official in Dhaka, the Bangladeshi capital.

According to the SITE Intelligence Group, which monitors radical Islamic websites, the Islamic State, also known as ISIS or ISIL, issued a statement later Monday claiming that a “security detachment” had tracked Mr. Tavella through the streets of Dhaka and then killed him using “silenced weapons.”