Men claiming to be part of a wedding party fired their automatic weapons into the air for 30 minutes outside St George's Syrian Catholic Church in the town of Bartella.
Local authorities failed to respond to the illegal incident which happened on 1st December 2018.
Meanwhile, a similar shooting incident took place outside a Syriac Catholic church in nearby Qaraqosh one week later.
The perpetrators identified themselves as members of the Popular Mobilisation Units, an Iran-backed paramilitary group which played a major role in the liberation of the Nineveh Plains from Islamic State (IS) extremists.
They also belong to the Shabak, a Shi'a Muslim ethnic group in Iraq which has been accused of infringing onto Christian villages through unlawful land purchases.
Middle East Concern (MEC), a Christian charity which promotes the freedoms of Christians throughout the region, said authorities had done nothing in response to the shootings.
A statement read: "To date, there have been no efforts to investigate these incidents, bring the perpetrators to justice or to protect the Christian community and church buildings in Bartella and Qaraqosh.
"Christians in Iraq strongly experience this as intimidation aimed at increasing their feelings of vulnerability and fear."
"The ancestral villages, where believers have been living since the early days of Christianity, are an important part of Iraqi Christians sense of identity.
"Recognising this, the Iraqi constitution prohibits changing land ownership if it will change the demographics of an area."
Efforts have intensified since last year to help Christian families resettle in the Nineveh Plains after IS was driven out of the region. Forty-per-cent have sinced returned.
MEC urged believers to pray for Iraqi Christians "to stand strong and be bold, in facing continued intimidations and threats".
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