The State Department said yesterday that Israel has been using U.S. supplied arms in support of Christian forces in southern Lebanon, but that this does not violate U.S. laws.

Spokesman John Trattner said "Israel informed us, but did not consult us" on its use of American weapons. Trattner would not say what weapons or military operations are involved, but Israeli Prime Minister Menahem Begin announced earlier this month that Israel has provided artillery support to Christian militiamen who are fighting against Palestinian forces.

Under U.S. arms export laws, Israel and other nations obtaining U.S. military equipment must agree to use it only for such purposes as self-defense and internal security. The State Department has concluded that the Israeli operations in southern Lebanon can be classified as self-defense, according to informed sources.

In obtaining U.S. military equipment, Israel and other recipients must also sign agreements not to transfer it to other countries without U.S. authorization. Asked if Israel has transferred U.S. arms to the Christian forces in Lebanon, Trattner replied: "Israel has assured us that it has not transferred to any party in the Lebanese, conflict any U.S. origin equipment which would fall under such an agreement." He would not elaborate. tr for add2.

Newsweek magazine, in its current issue, reported that Palestinian commandosin "America-made machine guns, M-16 rifles and mortars" that had been captured from rightist forces and that the hulks of three U.S. mae tanks destroyed in fighting la spring can be seen in the area.

State Department sources suggested yesterdat that U.S. equipmtnt might have been obtained by Christian militiamen from stocks of the Lebanese national army, by purchase from grey market arm suppliers in Europe or elsewhere, or from Israeli stocks of American-made weapons captured from Jordan in the 1967 war (and thus nosubject to U.S. sales restrictions).

The sources said that United States has asked for and received repeated Israeli assurances that American law is not being vilated in the military support that Israeli giving to the Christian militia in southern Lebanon.

On Aug. 9. Sen. James Abourezk (D.S.D.) sent letters to President Carter and Secretary of State Chrus R. Vance asking for an investigation into Israel's use of U.S. arms nsouthern Lebanon in ght light of Begin's statements. The State Department announcement yesterday was prompted bypressqueionson thsubject.