She was wearing a protective press vest and helmet.
“The US Justice Ministry's decision to investigate the unfortunate death of Shireen Abu Akleh is a serious mistake,” Mr Gantz said on Monday night.
Shireen Abu Akleh's funeral — in pictures
The US Justice Department and FBI declined to comment on media reports about an investigation.
The circumstances of Abu Akleh's killing remain heavily disputed.
Israel's military said in September that she was probably unintentionally shot by an Israeli soldier but could have also been hit by Palestinian fire.
Palestinian officials and Abu Akleh's family have said they believe she was killed deliberately by Israeli forces and have rejected Israeli statements that there were militants around where she was standing.
Other witness accounts of the incident have disputed that Israeli positions were under fire from the area where Abu Akleh was standing when she was killed.
One of the most recognisable faces reporting on the Israeli-Palestinian conflict for two decades, Abu Akleh's death triggered outrage across the world, worsened when Israeli police beat mourners at her funeral in Jerusalem.
“It has been six long months of my family and I advocating for accountability and justice,” her niece Lareen Abu Akleh said in a video posted on Twitter on November 11.
“We continue to pursue all possible avenues for accountability and we have hope that some day we will see justice for Shireen.”