President Carter believes the problem of the Palestinians on the West Bank of the Jordan River and in the Gaza Strip may be solved by beginning with an "interim solution" that would provide for the joint administration of those areas by nations involved in the Middle East dispute.

Under this proposal, the Palestinians eventually would be given the right to decide either to align themselves with Jordan or remain under joint Arab-Israeli administration.

Sounding optimistic about the progress in the Middle East peace negotiations, the President reiterated his opposition to creation of an independent Palestinian state on the West Bank and said that every Arab leader he talked to in the last two weeks fully supports the peace initiatives of Egyptian President Anwar Sadat.

Carter made the comments to reporters aboard Air Force One Friday night as he was returning to the United States from his tour of seven nations. The next of the interview was released by the White House yesterday.

Conceding that he made a few mistakes during the exhausting journey of 18,000 miles, the President pronounced the overall impact of the trip a success. He said:

"I wanted to project an image of a nation that stands for what is right and decent and good; strengthen the concept of democracy, both in the developing and developed nations; try to make progress on resolving the Middle Eastern dispute . . . These were the four or five things that I had in mind. I think we did a fairly good job."

The Middle East generally, an the issue the Palestinians specifically, dominated Carter's trip. He met with Sadat in Aswan, Egypt, and also held discussions with King Hussein of Jordan, the shah of Iran and King Khalid and other Saudi leaders.

Officially, the Arab nations of the Middle East are demanding that the palestinians have the "right of self determination," including the right to create an independent state of their own between Israel and Egypt.

What the President proposed in the airborne interview would provide for joint Arab-Israeli administration of the disputed territories, and after a while a decision by the Palestinians to either continue that arrangement or to align with Jordan.

Thus, the Palestinians would be given a limited right of self determination, but not the right to create an independent state - something the Israelis have vowed never to accept.

Conceding that the details of such a plan "are going to be a problem," the President said "there are no differences that separate us from Sadat." When he met Sadat last April in Washington, Carter said, the Egyptian president said he did not expect to see a Middle East peace settlement in his lifetime. When they met in Aswan last week, Carter added, Sadat said he had been "completely wrong" in that gloomy prediction.

The President also discussed India, calling his visit there "extraordinary," and took the blame for a gaffe that marred the warmth of his welcom in New Delhi.

The gaffe was Carter's comment to Secretary of State Cyrus R. Vance, inadvertently recorded by reporters, that the United States should send Prime Minister Morarji R. Desai a "cold, very blunt" letter about Indian's refusal to accept certain safeguards in connection with supplies for its nuclear power program.

"It was my mistake," he said "I should have said a very frank and factual letter.

But Carter said the incident did not damage his relationship with Desai and they had joked about it in New Delhi.

On other topics dealing with his trip, the President:

Said his visit to Poland convinced him that the Iron Curtain "is being parted." He said, "We are not trying to drive a wedge between those Warsaw Pact nations and the Soviet Union. But we are trying to get them to look to us as friends who want peace, who recognize the horrible suffering that they have experienced , and who are building a basis for friendship and trade and mutual exchange."

Asserted that the shah of Iran "is deeply concerned about human rights" and that in some aspects of human rights Iran has experienced considerable progress over the last 20 years.

Called the "outpouring of emotion and friendship toward us and the tremendous crowds" that greeted him in France "more than I had anticipated."

Predicted that another of the trip's well-publicized foulups - the mistranslation of his remarks at the Warsaw Airport - would have no lasting effect. He said he joked about it with Communist leader Edward Gierek, who told him, "In Poland, we don't criticize women or translators."

Carter said that despite the brutal schedule he was not tired until the last day in Brussels. But he suggested that future foreign travels may be less hectic, if only to preserve the physical well-being of his own staff and the press.

Of the trip genrally, the President said:

"It was a trip that was symbolic of the power and influence and the good-will of the United States. I tried to emphasize everywhere I went the concepts of morality and decency and goodness and friendship and human rights.

"So I didn't feel under any sort of uncomfortable strain to prove something that I don't really think our nation represents," he continued. "It was symbolic to that degree. It symbolized what American is, what America wants to be."