A man walks near a mural depicting slain Palestinian journalist Shireen Abu Akleh, on Israel separation barrier in the West Bank city of Bethlehem, Wednesday, July 6, 2022. AP
Their request came after they condemned a US probe which said it was not possible to determine whose gun fired the bullet which killed the Al Jazeera reporter.
A US citizen, she was shot in the head while covering an Israeli army operation in Jenin on May 11, despite wearing a vest that said "Press."
In a letter sent to Biden Friday morning, the journalist's brother Anton Abu Akleh said she was "murdered by an Israeli-fired bullet."
The family called on Biden to "meet with us during your upcoming visit and hear directly from us about our concerns and demands for justice".
Biden is to visit Israel and the occupied West Bank from July 13 to 15, and plans to hold talks with leaders on both sides before heading to Saudi Arabia in his first trip to the region since being elected president.
On Monday the US State Department said that Abu Akleh was likely shot from an Israeli position but that there was no evidence the killing was intentional and that the bullet was too damaged for a conclusive finding.
The letter expresses the family's "grief, outrage and sense of betrayal" over the Biden administration's "abject response" to Abu Akleh's death.
"Your administration's actions exhibit an apparent intent to undermine our efforts toward justice and accountability," the letter said, accusing the US of "skulking toward the erasure of any wrongdoings by Israeli forces".
The Palestinian Authority, which rules the Israeli-occupied West Bank, had reluctantly handed over the bullet to the United States and said it was not giving it to Israel, fearing a whitewash.
But on Monday, the Israeli army said in a statement that Israeli experts had done forensic analysis on the bullet in a laboratory in Israel.
State Department spokesman Ned Price insisted that two members of the team of the US Security Coordinator (USSC), which liaises with the Palestinian Authority on security assistance, carried out the examination.
Israeli Defence Minister Benny Gantz said Monday that it remained impossible to determine the source of the shooting "and, as such, the investigation will continue."
There was no immediate comment from the American embassy in Israel on the Abu Akleh family's requests.