By Yolande Knell
The attacks reportedly happened near Mount Harif military base in the Negev desert. Photo: AFP / Menahem Kahana
Three Israeli soldiers have been killed by an Egyptian security officer in exchanges of fire on the Israeli side of the border.
The armed forces of both countries say they are jointly investigating the unusual incident.
Egypt said its officer crossed into Israel while chasing drug traffickers.
The Israeli military has said the shootings were assumed to be connected with a drug smuggling operation it had thwarted overnight.
According to the army, two Israeli soldiers - a man and woman - posted in a remote spot along the border were shot dead early on Saturday morning.
Their bodies were discovered after a senior officer was unable to contact them by radio.
Hours later, after a search operation, the alleged attacker was encircled and there was a shootout, the Israeli military said.
A third soldier was killed, along with the gunman, who it said was an Egyptian policeman. Another soldier was wounded in that exchange.
In a vaguely worded statement, the Egyptian military said that its security officer was pursuing drug smugglers and that a shooting led to the Israeli deaths.
It also conveyed "sincere condolences" to the families of the victims.
The Israeli military said contraband worth about $400,000 was seized by its forces during the overnight operation against smugglers.
Soldiers are continuing to search in the area for others that may have been involved, the army said. It was not clear how the policeman managed to enter Israel from Egypt.
Israeli media said the attacks happened between Mount Harif and Mount Sagi - which lie in the Negev desert, about half-way between the Mediterranean coast and the Red Sea Egyptian resort of Eilat.
Israeli military spokesman Richard Hecht told journalists: "Co-operation with the Egyptians is ongoing, it's good. This is not geopolitical."
This appears to be one of the most serious border incidents since Egypt became the first Arab country to sign a peace treaty with Israel in 1979.
Although the two states are often described as having "a cold peace" in recent years, they have worked together closely on military and intelligence matters, particularly on counter-terrorism.
The Israeli air force has supported the Egyptian army in its fight against so-called Islamic State militants in the northern part of the Sinai Peninsula.
The most serious infiltration attempt in recent times took place in 2012.
Back then, militants attacked an Egyptian checkpoint near to Rafah on the border with the Gaza Strip, killing 16 Egyptian policemen and stealing two armoured cars.
They used these to break through the Kerem Shalom border crossing with Israel where one of the vehicles exploded. After a firefight, Israel said the bodies of eight attackers were found.
In the past decade, Israel has built a tall border fence to try to keep out militants and to stop people-smuggling from Egypt - in particular migrants crossing from sub-Saharan Africa.
However, drug smuggling attempts in the area remain frequent. The border stretches some 255 kilometres, making it difficult for security patrols.
Recent years have seen several cases of gunfire between smugglers and Israeli soldiers. The Egyptian army has also shot at drug smugglers and jihadists which has occasionally led to accidental cross-border fire.
Last December, Israeli soldiers shot dead a suspect who was apparently trying to smuggle drugs into Israel.
- BBC