In a statement posted on websites on Wednesday, the groups instead accused Iraq's national security adviser Mowaffaq al-Rubaie of involvement in the blasts.
"Any attempt to use these foolish explosions to attack the Mujahideen is doomed to fail," said the statement signed by the Mujahideen Information Centre.
"The level of these operations was much lower than those of the Mujahideen. If the Mujahideen had decided to attack these churches…would a single person walk out alive?" it said.
"Any attempt to use these foolish explosions to attack the Mujahideen is doomed to fail"
Mujahideen Information Centre
The centre said it spoke on behalf of three groups – Jihad Squadrons, Islamic Army Brigades and the Jihad Consultative Council.
It blamed al-Rubaie of involvement in the blasts with "the help of the Zionists and Americans."
The statement also said Islamic fighters would only attack Christians who helped occupiers or were proven to have committed treason, or spread corruption or proselytized.
In apparent coordinated attacks timed to coincide with evening prayers, car bombs exploded outside at least five churches on Sunday.
While four blasts hit churches in Baghdad, two hit churches in the northern city of Mosul.