Egypt´s army promised "revenge" on Monday after Islamist gunmen killed 16 of the country´s soldiers in the Sinai Peninsula and then launched a failed attack on Israel.

This was the bloodiest in a series of violent incidents on the frontier between the two neighbours.

The extremists managed to raid an Egyptian army base in the town of Rafah on Sunday night, killing the guards and stealing two vehicles, which they used to burst through the border fence and penetrate over a mile into Israeli territory.

The gunmen, who wore suicide bomb vests, were intercepted and killed by Israeli forces near the town of Yavul.

Since the onset of the protests against Hosni Mubarak´s regime in January 2011, the Sinai Peninsula has become increasingly lawless. Israel has accused Cairo´s new government under President Mohammed Morsi of failing to take control of the situation.

Thousands of European holidaymakers visit Egypt´s Red Sea resorts in Sinai, making the deteriorating security situation a danger to the country´s own economy, as well as to Israel.

Visiting the border with Egypt on Monday, Ehud Barak, the Israeli defence minister, said: "I hope that this will be a wake-up call for Egypt regarding the necessity to be sharp and efficient on their side."

A statement from the Egyptian army promised to "avenge" the soldiers who died, adding: "Egyptians will not have to wait long before they see a reaction to this attack by terrorists. Anyone liaising with these groups that have attacked our troops in the Sinai in recent months will pay dearly, be it inside Egypt or abroad."

An Egyptian security official said the assault on the army base had been a joint operation, mounted by extremists who entered the country through a tunnel from the Gaza Strip, along with others from Sinai. Hamas, the radical Palestinian group which controls Gaza, condemned the incident and denied any responsibility.

The highly sensitive relationship between Israel and Egypt will complicate the security response to the attack. Under the peace treaty between the two rivals, signed in 1979, Egypt can only deploy a limited force of border guards inside Sinai. Mr Morsi wants to ease the restrictions and deploy a sizeable military force – but Israel will be deeply reluctant to agree.

However, Israel´s own options are also constrained. If the country were to retaliate for any attack by striking inside Egyptian territory, this could jeopardise the peace treaty. The era of harmony between the two countries has been strained already by the election of a new government in Cairo dominated by the Muslim Brotherhood.

If, however, extremists striking from Sinai were to kill Israeli civilians, the country might take the risk. Under those circumstances, Yaakov Katz, from Jane´s Defence, a consultancy, said: "Israel would be hard pressed not to retaliate, even against targets in Egypt. The government would be under immense pressure to do so."

He added: "If Israel were to retaliate into the Sinai, this would a very slippery slope." (© Copyright of Telegraph Media Group Limited 2012. 08/07/12)