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The other two rockets hit residential neighborhoods near that area of the Iraqi capital, according to security sources.
The Green Zone is a sector of the Iraqi capital where the US embassy is located and is placed under high security.
This is the third attack in a week against the Western presence in Iraq, where a certain calm reigned in recent months.
More than a dozen rockets were launched a week ago at a military installation at an airport in Erbil, in Iraqi Kurdistan (north), where US troops are located, participating since 2014 in the coalition against the Islamic State (IS).
A foreign civilian employee was killed in the attack last Monday, which caused another fatality.
Another burst of rockets hit an air base north of Baghdad on Saturday, where most of the F-16 fighters that Iraq bought from the United States and used to fight IS sleeper cells are based.
This attack caused one injury, security sources told AFP.
