Reporting from the eastern al-Rustamiya district, Aljazeera sources said the attack on Tuesday was carried out at the same time as a similar raid on the Ministry of Culture.
Another bomb targeted a US convoy travelling in a street next to the Palestine and Sheraton hotels.
Iraqi police were unable to confirm if the attacks had resulted in casualties.
During the night on Monday, Iraqi resistance fighters fired a dozen mortars at central Baghdad's Green Zone compound housing the interim Iraqi government and the US and British embassies, Aljazeera's correspondent reported.
In the past week, fighters have stepped up mortar and rocket attacks in Baghdad.
A series of strong explosions were also heard in Baghdad early on Tuesday, coming from the direction of the Sadr City neighbourhood.
A curfew was imposed in Sadr
City after fierce fighting there
Shortly after the blasts, at about 7am (0300 GMT), US helicopters flew over Sadr City where a curfew was imposed on Monday after fierce fighting between followers of Shia leader Muqtada al-Sadr and US forces left many dead.
In Najaf, fresh fighting broke out on Tuesday, with explosions and gunfire coming from the heart of the city where Al-Mahdi army fighters are dug in.
Witnesses said US warplanes were flying overhead while smoke was rising from near the city's ancient cemetery, a haven for the fighters who have been battling US marines since last Thursday.
US troops called on Iraqi civilians to immediately evacuate areas where clashes with Al-Mahdi army fighters were intense, raising fears of a full-scale US-led offensive.
Soldiers in Humvee vehicles toured Najaf with loudspeakers and urged the population to leave the combat zone.
Meanwhile, Ahmad al-Shibani, al-Sadr's official spokesman in Najaf, told Aljazeera there was no truce with occupation troops. Fighting was continuing, he said.
"We are ready for any peaceful step. But we don't accept a false truce"
However, he said fighters hoped to reach a ceasefire and halt the bloodshed in the city soon.
"We are ready for any peaceful step," he said. "But we don't accept a false truce, full of hatred and envy, like the one proposed by the governor on Monday."
Drawing what he called "Najaf's military map", al-Shibani said the city was under the control of the Al-Mahdi army in the east, west and south.
The north, towards Karbala, has been under the control of US and Iraqi government forces and that is why there are continuing clashes in Wadi al-Salam cemetery in the north, al-Shibani said.
He added: "The cemetery is now under the control of the Al-Mahdi army. We escorted a number of media reporters and cameramen on Monday to the area to show that the cemetery is controlled by the Al-Mahdi army."