BAGHDAD—Powerful, coordinated bombs blasted three hotels catering to Westerners and shook a swath of central Baghdad, killing at least 36 people in the latest of four large-scale attacks challenging the government's ability to secure the country and its upcoming parliamentary elections.

The blasts came the same day the government announced the execution of Ali Hassan al-Majid, former leader Saddam Hussein's cousin, better known as Chemical Ali. There was no immediate indication of a link between the attacks and Mr. Majid's...