Several civilians were believed to have died in Thursday's first explosion that hit security officials as they were eating at al-Zahawi restaurant in an eastern district of the capital.
Speaking to Aljazeera by phone from Baghdad, Iraqi journalist Walid Khalid quoted witnesses and police as saying that a bomber targeted police officers who were having lunch at the restaurant in the Baghdad al-Jadida (New Baghdad) district, east of the capital centre.
"According to medics at al-Kindi and Ibn Sina hospitals, 13 people were killed and 56 wounded," he added.
The blast destroyed two buildings, five shops, stalls and 13 cars.
US forces who arrived at the scene after the blast fired random shots into the air to disperse the crowd while bystanders threw stones and empty bottles at them, Khalid said.
A lot of confusion prevailed in the area after US forces arrived, but matters settled down after Iraqi police took control, he added
Iraq is reeling from one of the
deadliest waves of bloodletting
Speaking to witnesses and police officials at the scene, Aljazeera reported that between 15 and 20 people died in the twin blasts.
Less is known about the second explosion, although Aljazeera learned that it took place in the vicinity of al-Samarai mosque in the same district.
Both attacks come after senior army officer Iyad Imad Mahdi was shot several times as he drove to work at the Ministry of Defence on Thursday morning in the western quarter of the Iraqi capital.
Mahdi was already dead by the time he arrived at Yarmuk hospital at 7.15am (0315 GMT).
And one hour earlier, unknown assailants also shot police Colonel Jamal Ahmed Hussein several times.
Hussein was killed as he set off for work at the Interior Ministry. He was gunned down in the al-Amin district in southeast Baghdad and died on arrival at the Kindi hospital.
Medical sources in Falluja have also reported the deaths of three members of the Iraqi National Guard and the injuries of several more after their patrol was attacked in the city's centre.
Elsewhere in Iraq, Aljazeera reported that a car bomb parked on the roadside in the al-Khadhraa district missed its target - a US military convoy - and wounded several Iraqis instead, five seriously.
Iraqi and US troops seem unable
to halt the escalating violence
Separately, a policeman and two civilians were wounded in two bomb explosions on a road near the northern Iraqi city of Kirkuk, according to Kirkuk police chief General Turhan Yussef.
Yussef said the first bomb exploded at about 9.20am on the road leading north and wounded a police officer, followed by a second bomb 2km out of town that injured a couple of civilians.
And the US military announced on Thursday that two marines were killed on Wednesday when their armoured vehicle drove over a mine in northwest Iraq during an offensive against fighters.
Three more US soldiers were killed on Thursday in bomb attacks in Baghdad and to the north and south of the capital.
Aljazeera has also learned that an Iraqi soldier and a civilian were killed in two separate attacks in the city of Samarra.
The assassinations and attacks come a day after at least 81 Iraqis were killed and more than 150 wounded in a series of bomb attacks in northern Iraq.
Elsewhere, a 1000-strong US force backed by aircraft battling fighters in the west of the country near al-Qaim in the past few days, claim to have killed up to 100 Iraqi fighters.