In an apparent move to allay Jordanian unease about the U.S. position on the Palestinian issue, the United States took the unusual step today of saying it "remains committed to Jordan's stability, territorial integrity and security."

Jordanian officials have been concerned by persistent suggestions by Israeli Defense Minister Ariel Sharon that the Hashemite kingdom, and not the Israeli-occupied West Bank and Gaza, should be the homeland of the Palestinians.

Jordan has been particularly worried ever since remarks made this summer by President Reagan to four Arab ambassadors in Washington that apparently were misconstrued and reported to King Hussein as veiled U.S. support for Sharon's provocative scheme, according to U.S. officials here. What apparently led to this conclusion was a reference by the president to the effect that the real issue was one of Palestinian refugees, not Palestinian land.

The U.S. reassurances were given to the Jordanian monarch by U.S. Ambassador Richard Veits, whose meeting with the king today was his first since he presented his credentials in August. The timing of the note is also significant, as King Hussein plans an official visit to Washington on Nov. 2.

The American statement of support sought to clarify Washington's position on Sharon's thesis that the Hashemite monarchy is an anachronism that should be allowed, or encouraged, to disappear so that Palestinians, who make up 60 percent of Jordan's population, can establish their homeland there.

Sharon has advocated such a solution -- which is contrary to the official thinking of Prime Minister Menachem Begin's government -- at least since 1975 if not earlier. What has shaken up Jordanians is that since becoming defense minister this summer and assuming Israel's second most powerful government post, Sharon not only has continued to talk about his plan, but, according to those who know him well, is actually studying its feasibility.

Reagan's remark about Palestinian refugees quickly spread through Jordan as proof that the United States really did not care about the parts of Arab Palestine occupied, and increasingly being settled, by the Israelis since the 1967 Arab-Israeli war. The reports have fed a national sense of insecurity that has accelerated since Israeli planes leapfrogged Jordan June 7 to bomb an Iraqi nuclear reactor near Baghdad.

The Jordanian monarch aired this concern in an interview early this month in the Paris-based Lebanese weekly Al Mostakbal in which he spoke of a "plot" for an Israeli occupation of Jordan that would allow the Palestinian issue to be solved on Jordanian territory, presumably, he hinted, with U.S. acquiescence.

"In my opinion," Hussein was quoted as saying, the United States is "searching for a situation in which Israeli hegemony can be expanded to include Jordan."

Privately, King Hussein and his aides have sought to portray the interview to Westerners as a case of the king's statement being taken out of context. But U.S. officials, who quickly had the interview translated, believe that was not the case.

In a prepared statement of clarification, Veits sought to reassure King Hussein, who, in an interview with The Washington Post earlier this week, showed increasing nervousness about just where the Reagan administration stands on basic Middle East issues.

"The Reagan administration, like its predecessors, is strongly committed to preserving the unique and enduring character of Jordan," the U.S. statement declared today. "The United States remains committed to Jordan's stability, territorial integrity and security. We believe that a secure Jordan, under your Hussein's leadership, will continue to be a moderate force in the region and continue its commitment to peace."

Whether that will be enough to counter Jordanian concern about Sharon's plan remains to be seen. Although many Jordanians believe Israel would not dare conspire to topple Hussein without U.S. approval, many others, including members of the government, are not so sure, noting that Sharon always has been unpredictable and that Israel is not beyond acting on its own without consulting the United States -- as it did in Baghdad.

"The statements he Sharon has made have indicated a commitment on his part to destabilize Jordan, to make it a springboard for further expansion of Israeli power and influence in the area," said the king's younger brother, Crown Prince Hassan, in an interview shortly before an official visit to Washington this week prior to delivering a speech at the United Nations. "Of course we have to take his views seriously. We know Israel is just waiting for a chance to act against us, as it has acted against Iraq and Lebanon."

Hassan said recent claims by Sharon that Palestine Liberation Organization guerrillas were again infiltrating into the Jordan Valley via Syria with heavy weapons were reason enough to suspect Sharon of "preparing a pretext that he could use for a military option in Jordan."

The crown prince said the Israeli charges were "unfounded," although Western diplomats say that at least twice in the last month Palestinian guerrillas did infiltrate through Jordanian Army security lines into the Jordan Valley, presumably from Syria.

On one occasion guerrillas are believed to have slipped into the West Bank to plant a mine, killing several Israeli soldiers, and another time guerrillas were arrested by Jordanian forces near Aqaba, where they were trying to set up Katyusha rockets to fire at the Israeli Red Sea port of Eilat.

The infiltrations seemed to have alarmed Jordan as much as Israel, and the lax security they demonstrated is believed to be at least one explanation why Hussein fired his armed forces chief of staff a month ago and the appointed Gen. Fathi Abu Taleb, previously the chief of military intelligence, to replace him. As one European diplomat here said: "The Jordanians are scared and nervous about Israel and don't want to give them any pretext for military action."