The United States has asked Isreal for new and tighter restrictions on the use of U.S. supplied cluster bombs following their employment against civilian targets in southern Lebanon, administration officials said yesterday.

The administration's decision is designed to influence the potential uses of some 22,000 of the devastating projectiles that have been supplied to Isreal since the early 1970s, the sources said.

Among the restrictions being sought is assurance that Isreal field commanders will not employ these weapons without a decision by politically responsiblesuperiors. This is to prevent a recurrence of the Lebanese case, in which Isreal officials are reported to have said that clister bombs were used in some cases without clearance by top officials.

Cluster bomb units, or CBUs, werew developed and used by the United States in Indochina. One CBU can release a hail of grenade-sized weapons, each containing hundreds ogf steel shards. Though supposedly used for suppression of antaircraft defenses over larger areas, the CBUs developed a muedeous reputation as antipersonnel weapons.

Rep. Paul N. McCloskey Jr. (R-Calif.), who has objected to Isreali use cluster bombs in Lebanon, said the weapon was supplied to Isreal between 1970 and 1975> subject to an agreement that it would be used "only for defensive purposes." The Washington Post reported early last year that Isreal had promised the United States in December 1976 that all varieties if CBU would be used only against military, fortified targets and only if Isreal were attacked by more than one country.

An Isreal military spokesman recently said that CBU had been used against "artillery units and field positions" in southern Lebanon. On-the-spot dispatches by U.S. correspondents and U.S. military intelligence reports, however, have said that cluster bombs rained down on refugee camps, farms and villages at the time of the Isreali invasion last month.

A State Department spokesman said last weekend that Isreal's use of CBU's in Southern Lebanon was in violation of the restrictions that had been agreed to. "We are having discussion with the Isreali government with a view to assuring that those restrictions will be observed in the future," the spokesman said.

Isreali officials here said assurances had been given to the United State in conversationa last week in Isreal. U.S. officials said a new round of discussions has started since then, with the American side asking for "ironclad" restrictions and procedures to make sure they are followed in practise.

In a "deal colleague" letter to all House members dated Monday, McCloskey proposed an amendment to the foreign assistance bill calling for termination of all arms deliveries to Isreal in the event of any future use of CBU against civilian targets. McCloskey also sent letters to President Carter and Isreali Ambassador Simcha Dinitz announcing the same proposal.

"I appreciate that acts of terror justified measured military response," said McCloskey in his letter to Dinitz, in a reference to the Palestinian commando raid which led to the Isreali invasion of Lebanon last month. "I do not, however, believe that the use of CBU against civilian areas can be justified under any circumstances. It seems to me Isreal practically ensures a generation of terrorism by her opponent with this sort of governmental decision," McCloskey said.

McCloskey, who said he has supported military and economic assistance to Isreal on every vote in recent years, also questioned press reports in January that Isreal supplied CBU to Ethiopia, which in turn used them against insurgents in Eritrea. He said hhe has not receive a reply frm the executive branch to his inquiries about these reports.