Mr. Lieberman and other Israeli officials offered no evidence to support the assertion.
Murtaja was shot while carrying a video camera and wearing a flak jacket marked with the word "press".
Rights groups have harshly criticised Israeli soldiers actions, and Palestinians say protesters are being shot while posing no threat to troops.
According to the Palestinian Health Ministry, at least 31 Palestinians have been killed by Israeli army cross-border gunfire since March 30, when peaceful rallies began along the Gaza Strip's eastern border with Israel.
In a statement pledging disciplinary action an Israeli Army spokesman said the incident took place took place on December 22, amid Palestinian unrest at U.S. President Donald Trump's recognition of Jerusalem as the Israeli capital. Hamas leader Ismail Haniyeh described a "battle for awareness" as he attended Murtaja's funeral Friday.
"We remind Israel of its obligations to ensure that excessive force is not employed against protestors and that in the context of a military occupation, as is the case in Gaza, the unjustified and unlawful recourse to firearms by law enforcement resulting in death may amount to a wilful killing, a grave breach of the Fourth Geneva Convention", Throssell said.
Instead, the cleric said that Hamas was deliberately using Gazans as human shields, a war crime under worldwide law, for political gains. The man who was shot is "suspected of organizing and leading this incident", the IDF said.
In the video that surfaced over the weekend, which appears to be filmed though a set of binoculars, the soldiers can be heard discussing the shot as the sniper takes aim.
"Judging soldiers because they are not expressing themselves elegantly while they are defending our borders is not serious", Bennett told army radio. It has said some of those at the border tried to damage the fence, planted explosives or hurled fire bombs.
Two Israeli right-wing ministers on Tuesday defended soldiers after a video appearing to show them shoot a Palestinian and rejoice in it spread widely on social media and news sites. Last week, officials estimated there were some 30,000 Gazans participating.