Lawyer Rodney Dixon said there had been a "complete cover-up" by Israel over Abu Akleh's death.
The Hague
TV network Al Jazeera submitted the case of slain journalist Shireen Abu Akleh to the International Criminal Court on Tuesday, saying she was killed by Israeli forces.
The Qatar-based channel said it had "unearthed new evidence" on the death of the Palestinian-American, shot while covering an Israel army raid in Jenin in the occupied West Bank on May 11.
Any person or group can file a complaint to the ICC prosecutor for investigation, but the Hague-based court is under no obligation to take on such cases.
Al Jazeera said its submission highlighted "new witness evidence and video footage (that) clearly show that Shireen and her colleagues were directly fired at by the Israeli Occupation Forces."
"The claim by the Israeli authorities that Shireen was killed by mistake in an exchange of fire is completely unfounded," the channel said.
An AFP journalist saw a lawyer representing Al Jazeera's case entering the ICC's headquarters to hand over their submission.
The ICC last year launched a probe into war crimes in the Palestinian territories, but Israel is not an ICC member and disputes the court's jurisdiction.
The Israeli army conceded on September 5 that one of its soldiers had likely shot Abu Akleh after mistaking her for a militant.
Israel said it would not cooperate with any external probe into Abu Akleh's death.
"No one will investigate IDF (Israeli military) soldiers and no one will preach to us about morals in warfare, certainly not Al Jazeera," Israeli Prime Minister Yair Lapid said in a statement.
The veteran reporter, who was a Christian, was wearing a bulletproof vest marked "Press" and a helmet when she was shot in the head in the Jenin refugee camp, a historic flashpoint in the Israeli-Palestinian conflict.
Her niece, Lina Abu Akleh, urged the ICC to investigate the journalist's death.
"The evidence is overwhelmingly clear, we expect the ICC to take action," she told a press conference in The Hague, adding that they had asked for a meeting with prosecutor Karim Khan.
"My family still doesn't know who fired that deadly bullet and who was in the chain of command that killed my aunt."
Lawyer Rodney Dixon said there had been a "complete cover-up" by Israel over Abu Akleh's death.
He alleged that her killing was part of a "systematic and widespread campaign" against Al Jazeera by Israel that also included the bombing of a Gaza building housing Al Jazeera's office last year.
"There's a clear attempt to shut Al Jazeera down and silence it." Dixon told the press conference.
"We are hopeful that there will now be justice for Shireen."
Dixon said they had not yet had a formal meeting with the prosecutor's office but had handed over evidence including some on memory sticks to the ICC's evidence unit.
After receiving complaints from individuals or groups, the ICC prosecutor decides independently what cases to submit to judges at the court.
Judges decide whether to allow a preliminary investigation by the prosecutor, which can then be followed by a formal investigation, and if warranted, charges.
In the majority of cases such complaints do not lead to investigations, according to the ICC.