JERUSALEM (Reuters) -Israeli Prime Minister Benjamin Netanyahu on Sunday called the killing of three soldiers by a member of the Egyptian security services a terrorist attack and demanded a full joint investigation with Cairo.

Egypt says it is working with Israel to investigate the incident which occurred on Saturday.

"Israel relayed a clear message to the Egyptian government. We expect that the joint investigation will be exhaustive and thorough," Netanyahu told his cabinet in televised remarks.

"We will refresh procedures and methods of operations and also the measures to reduce to a minimum the smuggling and to ensure tragic terrorist attacks like this do not happen again."

More details of the rare incident along the border emerged on Sunday. The frontier is usually peaceful, as the neighbours share close security cooperation, though there are frequent reports of drug smuggling, including one that took place prior to the deadly violence.

Israel's military said that two of its soldiers were shot dead early on Saturday by an Egyptian security services member who crossed through the border fence. Their desert post was remote and it took a number of hours before their bodies were discovered.

"From that moment a terrorist event was declared, leading to sweeps of the area," Israeli military spokesman Daniel Hagari said in an interview with Israel's YNET news. "A drone was sent up and 1.5 kilometres inside Israel a suspicious person was identified."

Soldiers then made contact and during an exchange of fire the Egyptian guard and a third Israeli soldier were killed.

On Saturday, the Egyptian military said the three Israelis and Egyptian guard had been killed in an exchange of fire as the guard chased smugglers across the frontier.

Two Egyptian sources said on Sunday that a team was examining the scene and the guard's body to determine how events transpired. Coworkers and family members of the Egyptian guard have been interviewed to figure out if he belonged to any political groups or suffered from mental illness, they said.

Egypt in 1979 became the first Arab country to sign a peace treaty with Israel and they share a more than 200-km (124-mile) long border.

(Reporting by Dan Williams and Ari Rabinovitch; Editing by Emelia Sithole-Matarise)