The Palestinians arrested a suspect in Monday's murder of Nuran Dib, on Tuesday evening.
The man reportedly fired shots into the air; one of those shots hit the girl.
The suspect is being questioned regarding the shooting.
The IDF said on Monday night that following an initial investigation, it did not seem that the 10-year-old from Rafah was hit by IDF tank fire.
Palestinians had originally claimed that the girl was killed by shrapnel fired from an IDF tank shell at an UNWRA schoolyard in Rafah, where Dib was playing.
The Palestinians used the supposed killing as a pretext to resume firing mortars at Gaza Strip settlements.
During the day Monday, soldiers positioned in posts located along the Philadelphi Route fired twice from light weapons into areas far from where the girl was hit, security officials said.
The officials said that at the time the girl was killed, officials at the District Coordinating Office received reports that in the same area Muslim worshippers returning from the Hajj in Mecca fired warning shots in the air to celebrate their return.
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