The Ministry of Interior said at least 35 people died and about 56 people were injured in the two bomb attacks, CNN said.
A car bomb exploded outside a church in the al-Dora district in southern Baghdad as worshipers were leaving after attending a Christmas Day service, CNN reported.
A second car bomb exploded in an outdoor marketplace frequented by Christians in the same district, police said.
There are an estimated 500,000 Christians in Iraq, the U.S. broadcaster said.
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