The family of Al Jazeera journalist Shireen Abu Akleh said Monday they were "incredulous" after the US reported it was not possible to determine whose gun fired the bullet which killed her.

The condemnation from the family of the prominent Palestinian-American reporter came after Israel said that its experts rather than American ones examined the bullet that killed Abu Akleh on May 11.

"With respect to today's announcement by the State Department -- on July 4, no less -- that a test of the spent round that killed Shireen Abu Akleh, an American citizen, was inconclusive as to the origin of the gun that fired it, we are incredulous," the Abu Akleh family said in a statement. 

The journalist, who held US citizenship, was killed while covering an Israeli army operation in the Jenin camp in the north of the occupied West Bank. 

"We will continue to advocate for justice for Shireen, and to hold the Israeli military and government accountable, no matter the attempts to obfuscate the reality of what happened on May 11," the statement added.

The Palestinian Authority had given the bullet extracted from Abu Akleh to US representatives on Saturday.

They said the Americans, but not the Israelis, could study it. 

But following the release of the US probe, Israel's army said: "A ballistic examination was conducted in a forensic laboratory in Israel.

"Israeli experts examined the bullet in order to determine the connection between the bullet and the weapon from which it was fired." 

US "representatives were present throughout the entire process," the army statement said. 

The United States said the veteran reporter was likely killed by gunfire from Israeli positions, but that there was no reason to believe her death was intentional.

Abu Akleh was wearing a vest marked "Press" and a helmet when she was shot in the head.

The State Department said that the US could not make a "definitive conclusion" on the origin of the bullet that killed her.

A senior PA official condemned attempts to "conceal the truth" over Abu Akleh's killing.

"We will continue our procedures at the international courts. We will not allow attempts to conceal the truth or to have shy references in pointing the finger of accusation (at) Israel," Hussein al-Sheikh wrote on Twitter.

Reacting to the US findings, Israeli Defence Minister Benny Gantz said "it is not possible to determine the source of the shooting –- and as such, the investigation will continue."