Tuesday's first blast targeted a parked Iraqi armoured vehicle and a car bomb went off minutes later at a nearby parking lot opposite the foreign ministry on the edge of the Green Zone.
Witnesses said a magnetic mine had been used in the first attack against the armoured vehicle parked at a security check point leading to the Green Zone.
Several cars were also damaged and Iraqi firefighters put out the flames before they could spread to other cars.
|The blasts, which occurred near the Green Zone, set ablaze several vehicles [AFP]
Minutes after the attacks, Negroponte began his scheduled news conference with Zebari.
Outside the Green Zone, soldiers fired in the air to keep motorists and pedestrians out of the bombed area.
The attacks in the central Salhiyah neighbourhood came despite stepped-up security checks on vehicles and followed a spate of bombings in the Iraqi capital last week.
The Green Zone has come under mortar and rocket attack in the past.
The US military claimed on Saturday it had killed an al-Qaeda fighter who planned some of the biggest bombings in Baghdad .
Mahir Ahmad Mahmud al-Zubaydi, also known as Abu Assad or Abu Rami, was killed along with an unidentified woman in Baghdad's Sunni district of Adhamiyah on Friday, the US military said.
Abu Rami was reportedly responsible for multiple car bombings and mortar attacks in Sadr City in 2006 and 2007, including car bombings in November 2006 that killed more than 200 people.
Negroponte is in Iraq for talks on the handover of security to Iraqi forces.
Washington and Baghdad have been in intense negotiations on a new agreement to allow US forces to remain in the country after a UN mandate expires at the end of this year.
However, a stumbling block has been the issue of who will be given jurisdiction to prosecute US troops accussed of crimes.
The US want the sole right but Iraq is holding out for some legal jurisdiction in order to maintain national soverignty.
Zebari said that "bold political decisions" were needed to resolve the issue.
He said that the US had submitted new ideas and legal language that "could be acceptable or reasonable", without giving details.
"I dont want to give you any false hope about where we are, but I think we are very close."
Negroponte did not give any details concerning the negotiations, but said that "both countries are pursuing this issue from the point of view of their own national self-interest."
Iraqi officials have said that a draft deal sees the US military leaving Iraq by the end of 2011, unless Baghdad asks them to stay longer.
Mahmoud Ahmedinejad, the president of Iran, told a visiting senior Iraqi official that Iraq had a "duty" not to make concessions to the US.
Also on Tuesday, an envoy to the Arab League arrived in Baghdad to head the grouping's mission there, and Iraqi foreign ministry official said.
It is the first Arab League envoy to visit Baghdad for 20 months and represents improving ties between Arab ststes and Iraq.