The bomber, wired with explosives, walked up to a group of about 100 Shi'ite mourners burying the victim of a drive-by shooting in the small town of Mukdadiyah, about 100 kilometres north-east of Baghdad, before detonating his bomb at the graveside.
Police said at least 34 people died and 48 were wounded in the attack. A hospital official said 37 people died and 45 were wounded.
The funeral was for a bodyguard who died overnight after being wounded in an attack on Wednesday on a local official of the Dawa party of outgoing Prime Minister Ibrahim Jaafari.
A young girl was also killed in the shooting although the target of the attack survived. The official, Ahmad al-Baqa, attended the funeral, surviving that attack too.
Security forces immediately cordoned off the town as families rushed to its overcrowded hospital looking for relatives. Army medics were drafted in to help treat the wounded.
Car bombs
In other violence, at least two car bombs exploded in the capital.
One blew up outside a police precinct issuing identity cards in a Shi'ite neighbourhood of north Baghdad. Five people were killed and 13 wounded, according to an initial toll.
Another car bomb exploded in south Baghdad as police commandos drove by. Two commandos and one civilian were killed and 11 people wounded.
A police commando was also killed and 18 others wounded in clashes with insurgents in the west of the capital, an official at Yarmuk hospital said. Many suffered shrapnel wounds.
A senior oil ministry official and his son were shot dead in their car in the same area of the capital. Their driver was wounded.
In central Baghdad, at least two people were wounded in a roadside bombing, while in the restive town of Baquba further north, one woman was killed and several people wounded in two bomb attacks.
In the mainly Shi'ite southeastern city of Amara, a former member of Saddam Hussein's Sunni-dominated Baath party was shot dead.
Convoy ambushed
The capital's fuel supplies came under renewed attack just days after deliveries resumed from Iraq's largest refinery.
Insurgents ambushed a convoy of up to 60 tankers being escorted by security forces to Baghdad from the refinery in the northern town of Baiji, killing a driver and three members of the convoy's security team.
In a separate attack in the afternoon, rebels torched three tanker trucks just north of Baghdad.
Deliveries of petrol and other refined products from Baiji had only resumed earlier this week after truck drivers walked off the job for nearly a fortnight to protest against insurgent death threats.
They only agreed to return to work after the authorities agreed to provide military escorts for tanker convoys.
The disruption led to fuel shortages not only in the capital but also across northern and north-central Iraq, sparking deadly riots in the oil city of Kirkuk.
Insurgent attacks and sabotage have virtually halted crude exports from northern Iraq as well as supplies for the domestic market.
But oil ministry spokesman Assim Jihad said exports from southern fields around Basra were back up to 1.55 million barrels per day (bpd), after a spate of bad weather in the Gulf briefly halted tanker liftings.
That disruption had brought exports down to 1.1 million bpd in December, the lowest level since the immediate aftermath of the 2003 invasion.
An international monitoring team, meanwhile, announced it would take up to three weeks to review complaints of fraud in last month's parliamentary elections.
It was unclear whether the team's work would delay publication of the final results of the December 15 elections, which are still not known nearly three weeks after the poll was held.
The foreign experts "will observe how the Independent Electoral Commission of Iraq dealt with the complaints it received, examine the system of data entry used in tallying votes and observe the field audits done by the IECI, as well as other election related matters," the commission said in a statement.
US troop reductions
Meanwhile, US President George W Bush, anxious to show progress in Iraq to Americans disenchanted by a war, said reducing US troops later this year may be possible.
He reiterated that any reductions would be based on the situation on the ground in Iraq and decisions by military commanders, not on a political timetable imposed by Washington, in a rejection of those Democrats demanding a phased pullout.
Mr Bush, speaking at the Pentagon, said a reduction of US troops already planned after the Iraqi election in mid-December was under way and would result in a net decrease of several thousand troops below the pre-election total of 138,000 US troops in Iraq.
He said the decrease came in addition to the reduction of about 20,000 troops who were in Iraq to help with security during the December elections.
"Later this year, if Iraqis continue to make progress on the security and political side that we expect, we can discuss further possible adjustments with the leaders of a new government in Iraq," Mr Bush said.