'The Baathists are behind these massive blasts,' said Zeinab al-Kanani, a parliamentarian affiliated with Shiite cleric Moqtada al-Sadr's movement.
'All these explosions in Baghdad reflect the security forces' negligence,' she said. 'The interior and defence ministries should review their security plans.'
Wednesday was the sixth anniversary of a powerful bomb attack at the UN headquarters in Baghdad's Green Zone that killed some 22 people. That bombing was the first large attack after US-led forces invaded Iraq and toppled the government of Saddam Hussein.
In recent months, attacks near the Green Zone have become rarer, and security has improved across the country.
According to the satellite news network al-Jazeera's count, 275 people died in insurgent attacks in July, down from 437 the month before.