The Reagan administration's secret offer to permit the Palestine Liberation Organization to participate in a Middle East peace conference has injected new tension into the U.S.-Israeli relationship.

At issue is whether the United States kept Israel informed about its plan to assure King Hussein of Jordan that the PLO could take part in the proposed conference if certain conditions were met.

Israeli sources insisted yesterday that U.S. officials made no mention of the subject during high-level contacts that included a meeting about the peace process between Israeli Foreign Minister Yitzhak Shamir and U.S. Ambassador Thomas R. Pickering three days after the American proposal was communicated to Hussein on Jan. 25.

However, U.S. officials, while refusing to discuss the matter directly, left the impression that Israeli Prime Minister Shimon Peres was aware of the U.S. move but had not been asked to endorse it. These officials said it would be "incorrect" to assume that no one in Israel knew about the Jan. 25 message.

Hussein brought the matter into the open Wednesday by announcing that he was breaking off talks with PLO Chairman Yasser Arafat about a joint Jordanian-Palestinian negotiating position. Hussein revealed that the United States, as a spur to the PLO, had given him "a written commitment" stating:

"When it is clearly on the public record that the PLO has accepted U.N. resolutions 242 and 338 recognizing Israel's right to exist , is prepared to negotiate peace with Israel, and has renounced terrorism, the United States accepts the fact that an invitation will be issued to the PLO to attend an international conference."

On Thursday, State Department spokesman Charles Redman confirmed that Hussein had spoken accurately. The proposal marked a clear-cut departure in American policy, which previously offered no role for the PLO as an organization in any phase of the peace process. The United States has said repeatedly in the past year that the Arab side in any peace talks should be represented by a joint Jordanian-Palestinian delegation without PLO participation.

Both Israeli and U.S. sources said last night that their governments were trying to keep the matter from causing an open rift. Israeli Ambassador Meir Rosenne met late yesterday with Michael H. Armacost, undersecretary of state for political affairs. Sources familiar with the session said Armacost had emphasized that the divisions between Arafat and Hussein had made the issue moot and thus not something that should cause trouble between Washington and Jerusalem.

This diplomatic episode could have serious implications for the stability of Israel's coalition government: an uneasy partnership between Peres' Labor Party, which accepts the possibility of a negotiated compromise with Jordan based on a trade of occupied territory for secure peace, and Shamir's Likud bloc, which opposes surrendering Israeli-occupied Arab territories.

The parties in the coalition formally agreed that the Israeli government would not engage in direct or indirect negotiations with the PLO. Over the past year, Israel has consistently opposed the idea of the United States dealing with the PLO or even meeting with a delegation of Palestinians who are not PLO members.

As a result, Israeli sources said, the U.S. statement to Hussein could pose domestic problems for Peres. If he did not know of the U.S. offer, he would be perceived in Israel as having been deceived by Washington. If he did know about the American shift and failed to object, he would be liable to charges of deceiving his government and abandoning its official position.

U.S. officials noted that Washington's offer includes the conditions that the United States long has said must be met before it would deal with the PLO. However, before the Jan. 25 offer, the United States had never explicitly stated that if the PLO satisfied those conditions it would gain admittance to the proposed peace conference.