An Egyptian security force member and three Israeli soldiers were killed in a rare clash near the border between the two neighbors, according to statements made by officials from both sides on Saturday.

The Israeli army said an Egyptian assailant shot dead two soldiers "in the early morning... while they secured a military post at the Egyptian border" on Mount Harif, near Mitzpe Ramon in the Negev desert.

The discovery of their bodies triggered a manhunt during which the third soldier was killed.

An army statement identified the assailant as an Egyptian policeman, saying Israeli troops killed him after being found "in Israeli territory."

The statement said an investigation was being carried out "in full cooperation with the Egyptian army."

The military added that a fourth Israeli soldier, a non-commissioned officer, was lightly wounded and evacuated to hospital.

An Egyptian army spokesperson said, "A member of the security forces ... chased drug smugglers. During the chase, the security agent crossed the security fence (border)," and an exchange of fire occurred.

Egypt was the first Arab country to make peace with Israel following the Camp David Accords of 1978, though there remains widespread popular opposition toward normalization in Egypt.

Their shared border is mainly peaceful, despite an insurgency in Egypt's Sinai Peninsula and occasional exchanges of fire between drug smugglers and Israeli forces.

Israel's army had initially declined to confirm media reports of the first two deaths while the families were being notified.

The two soldiers, a man and a woman, were "killed by live fire adjacent to the border," it said in a statement.

The woman was later identified as Lia Ben-Nun, 19.

Border incidents

A barrier runs along the Israel-Egypt border, and an army spokesman said Israel was looking into how it had been breached.

Hours before the deadly shooting, a spokesperson said that Israeli soldiers had foiled an attempted drug smuggling operation at the border, seizing contraband goods estimated to be worth 1.5 million shekels ($400,000).

The spokesman added that no link had been established between the drug seizure and the attack on the border post.

There have been several previous incidents along Israel's border with Egypt.

In 2011, assailants who entered from the Sinai killed eight Israelis in a triple ambush north of Eilat. Pursuing Israeli forces killed seven attackers and five Egyptian police.

In 2012, an Israeli soldier and three militants who infiltrated from the Sinai were killed in a clash along the border.

In 2014, two Israeli soldiers on patrol were wounded by unidentified men who fired an anti-tank weapon from the Sinai during an attempt to smuggle drugs.

And in 2015, rockets fired from the Sinai hit southern Israel without causing any casualties. The Daesh terrorist group later claimed responsibility.