Maj. Saad Haddad, commander of the Israeli-supported Arab militia in southern Lebanon for the past five years and undisputed leader of the tiny enclave he called the Republic of Free Lebanon for the last 2 1/2 years, resigned abruptly today and turned his command over to a subordinate officer.

Haddad announced his resignation in a radio broadcast, and said he would be succeeded by 1st Lt. Sharbal Baraqat, who was in the Lebanese Army officers' training school in Beirut during the 1976 Lebanese civil war but who was first awarded his commission by Haddad.

In a later broadcast, Haddad, 43, said he resigned primarily for health reasons. In April he was admitted to a hospital in Haifa complaining of chest pains, but doctors said he was suffering from exhaustion and nervous fatigue.

The announcement apparently came as a surprise to the Israeli Army's Northern Command, which supervises military activities in the border enclave. Israeli Army liaison officers reportedly were in Haddad's militia headquarters at Marjayoun tonight attempting to convince him to reconsider.

The Israeli Army command in Tel Aviv had no comment on the resignation. An Army command spokesman said, "I don't think we are going to relate to that."

Since the Israeli invasion of southern Lebanon in March 1978, Haddad's militia has served as a surrogate army for Israel, providing what was intended to be a cordon sanitaire across Israel's northern border to prevent Palestinian terrorist attacks against Israeli settlements in the upper Galilee region. Israeli troops have operated freely within the enclave, and Haddad has openly acknowledged coordinating his militia's activities with the Israeli defense forces.

Haddad, a Greek Catholic from Marjayoun with a long history of fighting Palestinians, commanded about 400 regular troops and about 1,000 village militia, most of them Shiite Moslems. Haddad has maintained that the enclave protects Christians seeking haven from the Moslem-Christian clashes in Beirut.

Haddad had recently complained bitterly about Palestine Liberation Organization violations of the July 24 Israeli-Palestinian cease-fire agreement in southern Lebanon, citing Israeli Army figures of 43 infractions, many of them directed against the Christian forces. He had complained that his hands were tied by the cease-fire, and his militias were not able to respond with artillery fire against PLO strongholds.

In his second broadcast, Haddad thanked the Israeli Army for its support.

On Sept. 24, he told the commander of the U.N. peace-keeping forces in southern Lebanon, Gen. William Callaghan, that his patience was "running out" and that he would retaliate against the PLO guerrillas.

However, U.N. officials said it has been quiet for some time in the south, with no serious breeches of the cease-fire since July 28.

Haddad was also reported to have been dissatisfied with recent changes within the Israeli Army liaison command and troubled by reports that the Lebanese Army command in Beirut had reactivated court-martial proceedings against him.

U.N. sources said tonight that Haddad's announcement came as a surprise to peace-keeping officers who regularly talk with him, and even caught by surprise Haddad's own officer corps.

A U.N. source in Naqura said that Baraqat last summer took command of the western sector of the 140-square-mile enclave. The U.N. official called Baraqat a "very responsible and serious young officer," and said that tension between the militias and UNIFIL troops in the western part of the enclave had diminished after Baraqat took command of the sector.

Baraqat, U.N. officials said, is still a member of the Lebanese Army, unlike Haddad, who was cashiered when he declared himself leader of the enclave in April 1979 and seceded from Lebanon.