Saudi Arabia has repeatedly told the Carter administration that it supports self-determination for the Palestinians, including their right to demand an independent state, foreign minister Saud al-Faisal said today in an interview.

His assertion, made in response to a series of questions, put Prince Saud in polite but clear disagreement with President Carter, who has said in recent months that no Arab leader has voiced support for a Palestinian state.

"Any interpretation of our position that says that we do not support a Palestinian state is erroneous," Saud said. "I cannot speak for other Arab leaders, but the Saudi position is clear. It is based on the right of the Palestinians themselves to determine whether they want an independent state, or an entity with links to another country, or another solution."

Speaking privately, other Arab officials have said that the remarks attributed to Carter have caused much consternation in the Middle East and have deeply embarrassed friendly Arab governments. This is reportedly especially true for Saudi Arabia's royal family, which has become a leading advocate of a U.S.-Palestinian dialogue.

But Saud elegantly masked any discomfort felt by the Saudis. He said that Carter's remarks had not created controversy between Washington and Riyadh, and added, "I don't put too much weight on a statement about this."

Saud is to meet Friday with Secretary of State Cyrus R. Vance.

The Princeton educated Saudi diplomat, who spoke today before the U.N. General Assembly, also made these points in the interview:

A comprehensive Arab-Israeli peace settlement that includes a solution to the Palestinian problem would bring normal relations between Israel and Saudi Arabia.He said that would not necessarily include diplomatic relations, but his formulation suggested an end to the present open hostilities between the two nations.

Saudi Arabia does not intend to extend beyond January its increase in oil production, currently at 9.5 million barrels a day, Saud said the increase was granted solely to provide balance to world oil markets disrupted by a temporary shortfall in Iranian production.

He will offer no public support for the announcement by President Carter Monday night that the United States would reinforce its naval presence in the Indian Ocean and accelerate formation of "rapid deployment forces" as part of the response to the quarrel with the Soviet Union over Soviet troops in Cuba. Saud said Saudi Arabia favors a reduction of both Soviet and U.S. military force in the Persian Gulf and Indian Ocean areas.

United States should eliminate "the immediate and direct danger" involved in the continuing Israeli attacks on southern Lebanon. His expression of concern came as the United States appeared to be gearing up for an important new effort to get the Palestine Liberation Organization and Israel to accept a reciprocal halt in military actions in southern Lebanon and across the Lebanese-Israeli border.

Lebanon's foreign minister, Fuad Boutros, also appeared to foreshadow the new U.S. effort by calling on the PLO in his speech today to the General Assembly "to channel its vitality and activity towards political diplomatic action and to undertake a positive initiative in this connection.

Arab sources said the Lebanese government is seeking agreement with the PLO for an effective guerrilla withdrawal from the south and cessation of raids on Israel as the first step in a firm truce. The agreement would be taken to an Arab summit, where Saudi Arabia would play a key role in determining Arab acceptance of the arrangement.

"Without a Lebanese-PLO accord, an Arab summit might be less productive and our position would have to be different," Boutros said in an interview.

Sauds put repeated and heavy emphasis throughout the hour-long interview on the positive benefits that he said the United States would gain by getting Israel to halt attacks on Lebanon and by launching a more comprehensive effort for a Middle East peace settlement that would directly involve the Palestinians.

He softly turned away questions that suggested that relations between the United States and the world's largest oil exporter have undergone serious strains because of Carter's commitment to the Camp David peace accords and the Egyptian-Israeli peace treaty, and the Lebanese crisis.

"The deep interference of Israel in the internal affairs of Lebanon is a dangerous new element, especially for the United States when Israel uses American-supplied weapons to carry out that interference," Saudi said. "Active U.S. involvement that produces concrete results will gain the respect and confidence of the Lebanese and then of the Arabs for the United States."

Speaking on the question of Saudi views toward a Palestinian state, the foreign minister said that Crown Prince Fahd had given President Carter "a position paper written by the Palestinians themselves clearly stating their views" during Fahd's May 1977 visit to Washington.

"The Palestinians know exactly what our position is. Our citizens know and so does the United States government. The Palestinians should be given the right to determine if they want an independent state and no one, including Saudi Arabia, should try to impose a solution on them."

Remarks attributed to Carter about the lack of Arab support for a Palestinian state apparently were intended to reassure Israel that it could be more forthcoming in the talks on autonomy for the West Bank and the Gaza Strip now being conducted by Egypt, Israel and the United States.

He reiterated Saudi opposition to the autonomy talks, which he said would fail because the definition of autonomy has been made by Israeli Prime Minister Menachem Begin and not by the Palestinians.

Saud showed reluctance to comment on Washington reports of plans to increase U.S. military presence in the Middle East. Criticizing the Soviet Union for its involvement in the region "through Cuba," Saud said that Middle Eastern nations were disturbed by "the bringing of the east-west conflict to their shores."