The blasts killed at least 31 people and wounded 71 others.
The twin attacks occurred during the morning rush hour in the mostly Shiite Kasrah section of the Azamiyah district in the northern part of the Iraqi capital.
Police said the first explosion damaged a minibus carrying the girls to school
and then a suicide bomber detonated an explosive belt in the middle of a throng that had gathered round the vehicle.
Kasrah is a bustling area of tea shops and restaurants, and home to a fine arts institute.
Male and female students, many of whom were having breakfast at the time of the strike, were among the dead and wounded, as were Iraqi soldiers and police who had rushed to the scene.
An interior ministry official speculated that extremists may have sought to "send a message" to Barack Obama, the president-elect of the United States, about "the real situation in Iraq", pressure the government not to sign a new security agreement with the US or embarrass the ruling parties ahead of regional elections in January.
In another attack, in Baquba, capital of the volatile northern Diyala province, a female suicide bomber killed five US-backed security patrolmen and wounded 11 other people, the US military said. Police said the bomber was a girl of 13.
The Baghdad blasts shattered storefronts along the crowded street and set more than a dozen cars on fire.
Abbas Fadhil, 45, was working in a restaurant nearby. "I saw several students trapped in a bus and screaming for help. We took the girls outside the bus and rushed them to hospital," he said, standing in front of the damaged restaurant – his shirt soaked with blood.
"This is a criminal act that targeted innocent people who were heading to work and school while the politicians are busy with their personal greed and ambitions."
The minibus was pock-marked with shrapnel marks with the floor soaked in blood. Girls' shoes were scattered amid the wreckage.
Ahmed Riyadh, 54, the owner of a nearby grocery, said the bombing was a "vicious attack" that "did not differentiate between Shiites and Sunnis". He continued: "We are fed up with such attacks and we want only to live in peace. The politicians should set aside their differences to stop the bloodshed."
No group claimed responsibility for the blasts, the deadliest attack in the Iraqi capital in weeks. But suicide attacks against Shiite civilians are the hallmark of al-Qaeda in Iraq, which maintains a limited presence in Baghdad despite military setbacks and the Sunni revolt against the terror movement last year.
US Colonel John Hort said the blasts were an "al-Qaeda trademark attack of a cowardly nature targeting civilians in Baghdad".
Violence is down significantly in Baghdad since the worst of the Sunni-Shiite fighting in 2006 and 2007. In recent weeks, however, there appears to have been an upturn in small-scale bombings during the morning rush hour – targeting Iraqi police and army patrols, government officials heading for work or commuters in an attempt to undermine public confidence.
Al-Qaeda and like-minded groups have been driven out of many parts of Iraq after local Sunni Arab tribesmen turned against them, but they are making a stand in northern areas such as the palm groves and orchards near Baquba.
US hopes new security pact will silence Shia critics
THE proposed US-Iraqi security pact removes language authorising Iraq to ask US soldiers to stay beyond 2011 and bans cross-border attacks from Iraqi soil, according to a newly revealed copy of the draft.
The latest draft, sent last week to Nouri al-Maliki, the prime minister, also strengthens language regarding Iraqi sovereignty, but does not appear to make significant changes in the limited legal authority granted to Iraq to prosecute US soldiers for major crimes committed off base and off duty.
It is unclear whether the changes are enough to silence critics – especially among the majority Shiite community – who have complained the deal favours the interests of the United States over those of Iraq.
Mr Maliki plans to show the draft to Jalal Talabani, the president, and his two vice-presidents. Later, he will submit it to the cabinet and, if the ministers agree, he will forward it to parliament for a final decision. That process could take more than a month.
Without an agreement or a new UN mandate, US military operations in Iraq would have to stop as of 1 January. The new draft states that US troops must be out of Iraqi cities by 30 June and leave the country entirely by 31 December, 2011. The previous draft authorised the Iraqi government to ask US troops to stay beyond that for training and other assistance. The draft also recognises the right of each country to remove US troops before that deadline.
The draft also gives Iraq the right to inspect and verify names of all US service members and contractors entering and leaving the country and provides for the US to take "appropriate measures" to deal with any threat to Iraq or its "democratic system and elected institutions".
The draft agreement also states that "Iraqi land, sea and air shall not be used as a launching or transit point for attacks against other countries".
Iraq insisted on the addition after last month's US raid into neighbouring Syria.