JERUSALEM, Sept 21 (Reuters) - Three armed militants slipped into Israel from Egypt's Sinai peninsula on Friday, killing an Israeli soldier and wounding another before being shot dead, the army said.

It was at least the fourth cross-border attack in just over a year - violence that has persisted despite an Egyptian army and police crackdown on Sinai militants begun last month.

The latest incident underscored deep Israeli concern about faltering security in Sinai since the fall of Egyptian president Hosni Mubarak in a democratic uprising in 2011. Israel is now building a fence along the desert border to improve security.

A big terror attack was thwarted, Israeli army spokeswoman Lieutenant-Colonel Avital Leibovich said of Friday's violence.

Three terrorists infiltrated from Sinai into Israel and opened fire towards IDF soldiers guarding the border. The terrorists were well armed and carried explosive belts upon their bodies, she added.

General Tal Russo, commander of Israeli troops in the region, said the gunmen ambushed soldiers who had just intercepted some African migrants trying to cross into Israel and were providing water to the group.

In the first round of fire, one of our fighters was killed, Russo told reporters near the scene. Another soldier was wounded by shrapnel when a gunman blew up due to an explosives vest he was wearing, the general said.

Russo said he had no information on the affiliation of the gunmen but promised an Israeli response for the attack once their identities were discovered. Previous attacks were blamed on Palestinian militants from Gaza and supporters believed to have established bases in the sparsely inhabited Sinai.

An Egyptian security source said one of the gunmen died when a bomb he was carrying detonated and the other two were killed in a gun battle with Israeli forces. He added that the nationalities of the gunmen were not immediately known.

Israel is putting up the border fence both to bolster security and curb an influx of African migrants, hoping to finish it by the end of the year. It will run along most of the 266 km (165 miles) from Eilat on the Red Sea to the Gaza Strip.

Leibovich said Friday's attack occurred about halfway down the border near an area known as Mount Harif, where the barrier is still under construction.

In June, militants fired on Israelis building a section of the barrier, killing a worker, before soldiers shot dead two of the attackers.

In August, Islamist gunmen killed 16 Egyptian border guards in north Sinai and hijacked an armored vehicle which they smashed across the border before being killed by Israeli forces.

Shortly afterward, Egypt sent hundreds of troops backed by tanks, armored vehicles and helicopters into the region in a joint operation with police to raid militant hideouts, arrest suspects and seize weapons.

(Additional reporting by Tom Perry in Cairo and Allyn Fisher-Ilan in Jerusalem; Writing by Ori Lewis; Editing by Crispian Balmer and Mark Heinrich)