Rocket fired towards Baghdad's Green Zone fell short of its target, damaged home and injured a child

Baghdad's Green Zone hosts the US, pictured, and other embassies (AFP)

According to Iraq's military, a rocket fired towards Baghdad's Green Zone, which hosts the US and other embassies, fell just short of its target, causing damage to a home and injuring a child early on Sunday,

The attack comes a little over a week since unprecedented arrests of Iran-backed militia said to have prevented similar incident

A military statement added that security forces at the same time stopped another Katyusha rocket from being launched at Taji military air base, north of the capital, which hosts US troops.

The Baghdad raid that put Kadhimi and Kataeb Hezbollah on a collision course. No known Iran-backed groups have claimed responsibility, Reuters reported.

A police and a medical source confirmed that a child had been slightly hurt and that it had been caused by rockets which landed in the home.

The police source reported that a system of anti-rocketing was created for the defense of the United States' Embassy and was tested on Saturday and fired a mid-air rocket before hitting the Green Zone.

The Iraqi security forces raided a headquarters of the Iran-backed Kataeb Hezbollah militia in southern Baghdad last week, arresting more than a dozen members of the group on charges of involvement in rocket attacks. Most of whom were released shortly afterwards.

Militias backed by Iran have come to dominate parts of Iraq's security institutions, economy and political life.

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Prime Minister Mustafa al-Kadhimi's government is favoured by the United States and has indicated it will back up tough talk against the militias with action.

The government labeled the operation pre-emptive as an attempt to "maintain the state's prestige" by stopping near-daily missile attacks on U.S. embassy and military bases hosting US troops for months.

But as reported on Thursday, Middle East Eye observers wondered whether it would really have the opposite effect and asked Kadhimi's gravity in tackling the semi-official armied factions of his country.