The barrage of seven rockets was spread over neighbourhoods in the mainly Shiite east of the Iraqi capital, striking as families gathered for the start of the weekend.
"Buildings have been flattened," a policeman told Reuters from one blast site. "There are still people trapped."
The mystery attack was the deadliest after several bloody days in Baghdad as militants defy a major security crackdown.
Along with the arrival of US reinforcements in a southern city where Iraqi troops and Shi'ite militia fought to a standstill this week, it underlined the scale of the task facing Shi'ite Prime Minister Nuri al-Maliki.
He said his new, US-trained forces would be able to take charge of security in most of Iraq by the end of the year.
Iraq’s Interior Ministry put the toll at 50 dead and said hospitals were struggling with about 200 wounded, a figure in line with other police sources. No official could say where the Soviet-made Katyusha rockets came from, or who fired them.
A website used by Sunni militants published a statement purportedly from al-Qaeda's umbrella organisation in Iraq. It renewed the sort of call for a holy war on the Shi'ite majority that many fear could help provoke all-out sectarian civil war.
Bush on Iraq
In the first of several speeches round the fifth anniversary of the September 11 attacks on New York and Washington, Mr Bush told military veterans in Salt Lake City: "If America were to pull out before Iraq could defend itself, the consequences would be absolutely predictable and absolutely disastrous. We would be handing Iraq over to our worst enemies."
"They would have a new sanctuary ... with huge oil riches," Mr Bush said. Opposition Democrats, eyeing gains in November's elections to Congress, are pushing for a timetable for US withdrawal.
Confirming British and Italian troops would hand over a second Iraqi province, Dhi Qar, to local security forces in September, Mr Maliki said earlier: "By the end of the year we hope that security in most of the provinces will be handed over."
He has said before Iraqis may be running all but Baghdad and the violent Sunni region of Anbar this year, a target many US analysts see as ambitious, at least in terms of real control.
A US force including heavy armour and dozens of vehicles rolled into Diwaniya, where Iraqi troops this week battled militiamen loyal to radical Shi'ite cleric Moqtada al-Sadr.
One Iraqi officer said he counted 70 US vehicles as well as helicopters arrive at the Polish-run Echo base in the city on Thursday. US and Iraqi commanders have vowed to pacify Diwaniya.
Another American soldier was killed in Anbar yesterday, taking the US death toll since the 2003 invasion to 2,638.
But the US commander, General Georgy Casey, assured Iraqis of a "substantial presence" by his forces until Iraqis felt ready to take over. He said that might be in 12 to 18 months but would not be drawn on when Americans would leave.
Four police commandos were also killed and 11 people were wounded when a bomb blasted their patrol in eastern Baghdad.
And British diplomats escaped unscathed when their convoy was struck by a roadside bomb in western Baghdad, damaging two vehicles.
US force at 140,000
Meanwhile the Pentagon announced the US has expanded its force in Iraq to 140,000 troops, the most since January and 13,000 more than five weeks ago, amid relentless violence in Baghdad and elsewhere.
The announcement follows July's decision by commanders to augment the US military presence in Baghdad to try to curb escalating sectarian violence that has heightened concern about all-out civil war in Iraq.
Lt Col Barry Johnson, a military spokesman in Iraq, said there are now about 15,000 US troops operating in Baghdad.
A defence official, speaking on condition of anonymity, said the US force likely will remain at about the current level in the coming months, but could shrink a bit by the end of the year depending on conditions in Iraq.