Al Jazeera's Owen Fay, reporting from Baghdad, said that the bombings appeared to be a response to an operation by the so-called Awakening Councils of Sunni fighters and the Iraqi military in the area.
"They claimed that they had killed 20 al-Qaeda in Iraq members, we are still waiting on exact confirmation of the numbers, so it appears that this attack was a retaliation," he said.
"It was a particularly brutal retaliation, one that has happened in an area that over the past 11 days has seen a great deal of activity.
"Al-Qaeda in Iraq is very much back on the case, very much back in action and it is a major concern to the government."
The twin bombings north of Baghdad came after a car bomb exploded in the centre of the capital, killing at least nine people and wounding more than 23 others, security officials said.
The bomb went off in al-Sinaa Street in the central Karrada neighbourhood, they said, adding that the blast happened at around 9:30am (06:30 GMT) as a US military patrol passed through the area.
Lieutenant-General Lloyd J Austin III, the second most senior US commander in Iraq, said last week that al-Qaeda in Iraq was trying to regroup after suffering a being dealt a blow by the Awakening Councils.
The bombings came as clashes between Shia fighters and Iraqi troops, backed by US forces, continued in Baghdad's Sadr City neighbourhood.
At least 18 people were killed on Thursday, according to the US military.Iran delegation
Iraq's government has sent a delegation of five politicians to Iran with what they say is evidence that Tehran is arming and training the Shia militias.
Reda Jawad Taqi, a Shia politician and a senior member of the Supreme Islamic Iraqi Council, confirmed that the delegation left for Iran on Wednesday.
Taqi did not provide details, but said the purpose of the trip was "to review the current situation in Iraq with Iranian officials, to clarify the
situation with them and to enhance the mutual relationship between the two countries".
Muqtada al-Sadr, the leader of the al-Mahdi Army militia, is believed to be in Iran, but his spokesman in the Iraqi city of Najaf said that he will not meet the Iraqi delegation.