The family said it was calling for the United States to launch its own "thorough, credible independent and transparent investigation" into Abu Akleh's murder.
The family of slain Palestinian-American journalist Shireen Abu Akleh has pressed the United States for an independent probe and accountability from Israel on a visit to Washington at the invitation of Secretary of State Antony Blinken.
"For far too long, the United States has enabled Israel to kill with impunity by providing weapons, immunity, and diplomatic cover," Shireen's brother Tony Abu Akleh and her niece and nephew said in a statement on Tuesday.
"Impunity leads to repetition. We are here to do our part to ensure that this cycle ends," they said.
"If we allow Shireen's killing to be swept under the rug, we send a message that the lives of US citizens abroad don't matter, that the lives of Palestinians living under Israeli occupation don't matter, and that the most courageous journalists in the world, those who cover the human impact of armed conflict and violence, are expendable."
Criticising Israel for using force
Shireen Abu Akleh, an Al Jazeera journalist and a prominent Palestinian reporter, was killed on May 11 as she covered an Israeli operation in the occupied West Bank.
The United States on July 4 released a statement saying she was likely shot by Israeli fire but that there was no evidence her killing was intentional and that the bullet was too damaged for a conclusive finding.
The statement outraged Abu Akleh's family and Palestinian leaders who say that the United States is not seeking accountability from Israel over the death of the journalist, who also held US citizenship.
Israel says it is still probing her death and rejects suggestions it targeted a journalist.
Abu Akleh's family unsuccessfully sought to meet President Joe Biden when he visited Israel and the occupied West Bank earlier this month.
Blinken, however, invited the family to visit Washington, National Security Advisor Jake Sullivan said during the trip.
Blinken had spoken earlier to her family by phone and publicly criticised Israel for using force at her funeral, when police grabbed Palestinian flags and pallbearers struggled not to drop her casket.