The strikes are the latest in a months-long surge of violence that is raising fears Iraq is slipping back toward the widespread sectarian killings that followed the 2003 US-led invasion a decade ago.
The attack on the funeral happened around dusk in the densely populated Shiite neighbourhood of Sadr City in northeastern Baghdad.
Police said at least 30 people were killed and more than more than 50 wounded when the bomber smashed his car into the tent before setting off its deadly payload. The explosion set several nearby cars on fire, sending a towering plume of thick black smoke over the city.
In that attack, police said four suicide bombers stormed a base for police commandos. Guards managed to kill one suicide bomber, but the three other bombers were able to set off their explosive belts inside the compound, police said. Beiji, a centre for oil refining, is 250 kilometres north of Baghdad.
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The police said that most of the members of the commando unit were not in the compound at the time of the attack because they were carrying out a security operation outside the city. Casualty figures would have been higher had they been inside, the police said.
Medics in nearby hospitals confirmed the casualty figures. All officials spoke on condition of anonymity because they were not authorised to speak to media.
There was no immediate claim of responsibility for the day's attacks. Al-Qaeda's local franchise in Iraq frequently targets Shiite civilians and security forces in an attempt to undermine public confidence in the Shiite-led government.