JERUSALEM/CAIRO (Reuters) -A member of Egypt's security forces was killed in a shooting incident near the Rafah border crossing between Egypt and the Gaza Strip and an investigation is under way, Egypt's military spokesperson said in a statement on Monday.

Israel's military had earlier said it was investigating reports of an exchange of fire between Israeli and Egyptian soldiers.

"A few hours ago (Monday), a shooting incident occurred on the Egyptian border. The incident is under review and discussions are being held with the Egyptians," the Israeli military said in a statement.

Israel seized control of the Rafah border crossing from the Gaza side of the border earlier this month as it stepped up its military offensive in the area, drawing strong criticism from Egypt.

Egypt is worried that Palestinians could be displaced from southern Gaza by the offensive, and has also repeatedly accused Israel of holding up deliveries of humanitarian aid to the territory, something Israel denies.

Egypt and Israel signed a peace treaty in 1979 and have cooperated closely on security issues around the borders between Israel, Egypt's Sinai Peninsula, and the Gaza Strip. They jointly upheld a blockade of Gaza after Hamas took control of the territory in 2007.

Security incidents between the two countries have been rare.

In October 2023, two weeks after the start of the war in Gaza, Israel said one of its tanks had accidentally hit an Egyptian position near the border with Gaza, and Egypt said several Egyptian border guards sustained minor injuries.

In June 2023, three Israeli soldiers and an Egyptian security officer were killed in a clash at the border.

(Reporting by James Mackenzie in Jerusalem, Nafisa Eltahir in Cairo and Jana Choukeir in Dubai; Writing by Aidan Lewis;Editing by Alison Williams)