In a message posted on Islamist websites, the Al Qaeda network in Iraq said Tuesday"s bombing targeted Shias and "apostates".
"We struck at a group of Shias and apostates who sold their faith for money and are a tool in the war on Iraqi Sunnis," said the statement.
It said it was "farcical" to say the capital was secure and that any measures put in place were no obstacle to its fighters.
After the bombing, which took place during the holy Muslim fasting month of Ramadan, Iraq"s two main political groups broke off talks on the formation of a government.
The negotiations have spluttered on since March elections without success, creating a political vacuum. It is feared militants are exploiting this vacuum in a bid to destabilise Iraq, where US combat operations in the month of Aug.