The explosion went off at a crowded market in the poor Shia district of Sadr City at about 10am and scorched many nearby cars.
Sources at the interior ministry said the number of deaths had risen to 62 during the morning, with 114 people wounded.
Nizar al-Samaraei, an Iraqi journalist, told Aljazeera the market was busy as it was the first day of the week when citizens usually go shopping.
A statement by The Supporters of the Sunni People posted on a website regularly used by Iraqi groups said: "Every day the world sees what rejectionist (Shia) militia ... do to the Sunni folk in Iraq with blessing and support from the rejectionist government led by [Nuri] al-Maliki.
"You have started and here we answer your aggression," said the statement whose authenticity could not be verified.
The new national unity government of al-Maliki, the prime minister, has imposed a security clampdown on the capital for the past three weeks.
The US military said on Friday the number of attacks had risen in that time, despite the killing of Abu Musab al-Zarqawi, the al-Qaeda in Iraq leader at the beginning of June, and widespread follow-up raids and arrests.
As more security force patrols were on the streets, more attacks on them were being made, a US officer said.