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 United Nations mandate expires at the end of this year.
Both sides say the "deal is close".
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.
|The blasts set ablaze several vehicles [AFP]
Several cars were also damaged and Iraqi firefighters put out the flames before they could spread to other cars.
Minutes after the attacks, Negroponte began his scheduled press 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.
Also on Tuesday an envoy to the Arab League arrived in Baghdad to head the groupings 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.