Israeli troops at a border crossing on Monday shot dead a Palestinian-Jordanian judge who allegedly tried to snatch a soldier's weapon, prompting Amman and the Palestinian Authority to demand an investigation.

The shooting took place on Monday morning at the Allenby Bridge crossing between the West Bank and Jordan, with the Israeli military saying troops had opened fire after a man tried to snatch a weapon from one of its soldiers.

The Western-backed Palestinian Authority sharply condemned the incident and Amman summoned the Israeli charge d'affaires to protest, demanding an "immediate investigation."

An Israeli army statement said "a Palestinian attempted to seize the weapon of a soldier at the Allenby Bridge crossing from Jordan".

"In response the forces at the scene opened fire towards the suspect. A hit was identified."

Palestinian security officials identified the man as 38-year-old Raed Zeiter, and Amman confirmed he also held Jordanian nationality.

A Jordanian security official confirmed to AFP that Zeiter worked as a judge in Amman and had left for the West Bank early on Monday. Jordan's justice ministry said he worked at a magistrates court in the capital.

Nazmi Muhanna, the Palestinian official in charge of border crossings, told AFP they were questioning around 50 people who had been with Zeiter on the bus carrying travellers from the Jordanian side to the Israeli side of the crossing.

"We are investigating with all the witnesses who were on the same bus. We will verify everything," he said.

"There are no surveillance cameras there so we cannot get to the truth without the witnesses who were on that bus."

Jordan's foreign minister summoned the Israeli charge d'affaires to "strongly condemn" the shooting and demand an immediate probe, a statement said.

"The Jordanian government is expecting a comprehensive report on the incident from the Israeli government. Jordan wants an immediate investigation without any delay," a statement quoted Foreign Minister Nasser Judeh as saying.

The Palestinian Authority also strongly condemned the incident and demanded an "international investigation" into the circumstances of Zeiter's death.

Palestinian security officials said Zeiter was originally from the northern city of Nablus in the Israeli-occupied West Bank, but had left the territories in 2011 and not returned.

Zeiter, who leaves behind a wife and two young children -- one of whom is in a coma in hospital -- was to be buried in Nablus on Tuesday morning, his family said.

Around 200 people demonstrated outside the Israeli embassy in Amman, demanding the Jordanian government expel the Israeli ambassador.

"We don't want a Zionist embassy on Jordanian territory! Down with the peace agreement" between the two countries, they chanted.

Zeiter's father said he was in shock over the shooting.

"We did not know that Raed was in the West Bank. I went to the court to check if he was working and I was told that he did not go to work today," said 70-year-old Alaa Zeiter, himself a former judge.

"My son is peaceful and professional. I am shocked," he told AFP by phone, before breaking down in tears.

Zeiter and his wife left later on Monday to travel to Nablus for his son's funeral.

The shooting was a rare incident of violence at the crossing, which is located in the Jordan Valley, just east of the Palestinian oasis town of Jericho.

The crossing, which lies 50 kilometres (30 miles) west of Amman, is also known as the King Hussein Bridge.

The terminal was closed after the incident but reopened later, an Israeli official said.