Stalls and soft-drink stands were destroyed by the explosion. Two passers-by were killed and eight others wounded, a police official said.
Karrada, a predominantly Shia area in central Baghdad, had been relatively calm in recent weeks after the so-called US security crackdown in the capital.
The army recruits killed near Haswa were Sunni Arabs from the western Anbar province that had just joined the Iraqi security forces.
They had been at a recruitment centre in the town of Fallujah earlier in the day.
Tribal leaders in Anbar have rounded up thousands of young men to join local security forces.
The shift by tribal elders last year towards supporting the interim Iraqi government forces has sparked a power struggle with foreign and anti-government fighters in the province.
The attacks came a day after more than 150 people were killed by a lorry bomb in a crowded market in the northern Iraqi village of Amirli, an Iraqi military commander told Al Jazeera.
Many homes in the small community were destroyed on Saturday when a suicide bomber detonated a powerful bomb on a lorry, security and administration officials said.
Residents and emergency workers continued to dig for bodies under the rubble on Sunday as relatives buried their dead.
|The bombing in Amirli was the second deadliest|
since the US-led invasion [AFP]
"I can't comprehend what has happened. My entire family was killed in one moment," Abbas Kadhim, who told Reuters new agency the blast levelled his house, killing his wife, his two sons, his parents and also a brother, said.
"There is no value left in my life ... I have asked God why I didn't just die with them so I wouldn't have to go through this torture."
The death toll made it the second deadliest bombing since the US-led invasion in 2003. In March, a truck bomb attack killed 152 people in the northern town of Tal Afar.
"I just visited the scene. It looks like an earthquake happened there," Shalal Abid al-Ahmed, a member of the Salahuddin provincial council, said.
Meanwhile, The New York Times newspaper called for US troops to leave Iraq now, writing the US plan to stabilise the country through military means is a lost cause.
"It is time for the United States to leave Iraq, without any more delay than the Pentagon needs to organise an orderly exit," it wrote in a rare, single-issue editorial taking up one-half of a page.
"Like many Americans, we have put off that conclusion, waiting for a sign that President Bush was seriously trying to dig the United States out of the disaster he created by invading Iraq without sufficient cause, in the face of global opposition, and without a plan to stabilise the country afterward."
The Times concluded that Bush has "neither the vision nor the means to do that."