Jordan said it partially reopened its border crossing with the Israeli-occupied West Bank on Sunday, three days after closing it following an attack that killed two Israeli soldiers.

"The crossing reopened Sunday for travellers only, while the movement of cargo trucks remains suspended until further notice," an official statement said.

Broadcaster Al-Mamlaka reported heavy traffic in both directions from early in the morning.

The Allenby Bridge crossing, also known as the King Hussein Bridge, is the only gateway Palestinians in the West Bank can use to travel abroad without passing through Israel, which has occupied the territory since 1967.

On Thursday, a Jordanian truck driver carrying aid for Gaza opened fire at the crossing, killing an Israeli soldier and a reserve officer with the civil administration before being "neutralised", according to Israel.

Following the attack, the Israeli military asked Jordan to suspend the transfer of aid through the terminal.

Jordan said it had launched an investigation and identified the assailant as Abdel Mutaleb al-Qaissi, 57.

It described him as "a civilian who had been working for three months as a driver delivering aid to Gaza", which the UN says is suffering from a humanitarian crisis after nearly two years of devastating war. (AFP)