There was no immediate claim of responsibility for Thursday's attack in Falluja, located 50km west of Baghdad.
Police said the funeral was for a local businessman opposed to al-Qaeda in Iraq.
"Let the people of Iraq vote if they want the US to stay or leave"
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The group is waging a campaign of bombings and shootings against Sunni Arab tribal leaders, politicians and others in western Anbar who have formed an alliance against them.
The bomber hit mourners in a funeral procession for Allawi al-Isawi, who had been killed earlier on Thursday, police officer Jamal Anfous said.
As mourners walked down a street holding aloft Isawi's coffin, the bomber drove into the crowd and blew himself up.
Ahmed al-Ani, a doctor at a local hospital, said 27 were killed and more than 30 wounded. Another hospital source put the death toll at 30.
In other violence on Thursday, a suicide bomber detonated a bomb aboard another small bus driving through Baghdad, killing three civilians and injuring eight others, police said.
And in Sulaiman Bek, 120km south of the northern city of Kirkuk, a roadside bomb killed six members of an Iraqi police convoy, police said.
Meanwhile, in Washington, the US president said the summer would be critical for his troop build-up strategy in Iraq.
George Bush said at a news conference that he expected "heavy fighting in the weeks and months" ahead, with more American and Iraqi casualties.
|Bush said the US commander was to report|
back on the security strategy's results [AFP]
Asked how long he believed he could sustain the policy without significant progress, Bush noted that General David Petraeus, the US commander in Iraq, was to report back on the results of the new strategy at the end of the summer.
A major security crackdown is focused on Baghdad, epicentre of sectarian violence between majority Shias and minority Sunnis.
Tens of thousands of US and Iraqi troops have been deployed and casualties are rising.
On Thursday, the US military announced that two American soldiers were killed the day before while conducting combat operations in Anbar.
Those deaths took the US death toll for the month to at least 82.
In Baghdad, the Iraqi prime minister presented the names of six new ministers to parliament on Thursday as part of what analysts say is an overdue shake-up of a weak and divided cabinet.
Nuri al-Maliki asked parliament to approve his candidates to fill vacancies left by members of the movement of Moqtada al-Sadr, the Shia leader who quit the government in April in protest at his refusal to set a timetable for a US troop withdrawal.
Al-Maliki withdrew his first list of candidates after some politicians complained they were too close to him.
He had promised to appoint technocrats to counter complaints that ministries are poorly run and have become personal fiefdoms for parties in his coalition government.