Sunday's blasts occurred at the offices of the Kurdistan Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK) in the northern city of Arbil. The two parties control the mainly Kurdish northern provinces.
By early evening Kurdish officials said the death toll stood at 56 with more than 200 others injured. One minister said the death toll could reach 100.
Hundreds had gathered at both party offices to mark the start of Eid al-Adha feast, a major Islamic holiday.
The dead included the governor of the region, ministers in the local administration and several senior officials, said Muhammed Ihsan, the minister for human rights for the Kurdish regional government.
Morgue director Tawana Karin was quoted by the Associated Press as saying at least 57 bodies were brought to the morgue.
The two bombs went off within five minutes of each other, at the two offices in the centre of Arbil, 10km apart.
"On the first day of Eid we receive people and well wishers and that's why security wasn't as tight as during the rest of the days"
minister for human rights for Kurdish regional government
"These figures are estimates but I believe about 60 people were killed at the PUK and about 80 at the KDP. There are a tremendous number of injured," said Muhammad Ihsan, minister for human rights for the Kurdish regional government.
"On the first day of Eid we receive people and well wishers and that's why security wasn't as tight as during the rest of the days," he said.
Ihsan said the dead included Arbil Governor Akram Mintik, Deputy Prime Minister Sami Abd al-Rahman, Minister of Council of Ministers Affairs Shawkat Shaikh Yazdin and Agriculture Minister Saad Abd Allah.
Officials were greeting people when the attacker approached them and detonated the explosives strapped around his body.
Occupation US military officials had said they were prepared for any upsurge of attacks coinciding with the holiday.
Kurdish leaders supported US-British efforts to oust Iraqi leader Saddam Hussein in the run-up to the March invasion.