Former president Jimmy Carter called on President Reagan yesterday to extend the limits of the SALT II nuclear arms treaty when it expires Dec. 31, saying that failure to do so "would be a very negative signal to the world that our interest in arms control is not sincere."

Carter, who negotiated and signed the unratified 1979 treaty with the Soviet Union, said his first preference would be for Reagan to ask for Senate ratification of the treaty and to propose to Soviet leader Mikhail Gorbachev that the document be extended for five years.

Carter said in an interview that this "wouldn't be an embarrassing reversal for the Reagan administration" even though Reagan consistently opposed SALT II, because the administration for the past four years has been pledged not to undercut the treaty.

If Reagan declines to seek ratification and a formal extension, Carter said, "a verbal agreement could be reached quite easily with the Soviets that the terms of the treaty be extended and observed on both sides, as has been the case in the last five years."

Any clear departure from the SALT II limits, whether before or after its expiration date at the end of this year, Carter said, would mean removal of limits that have been deemed advisable "even by Reagan" and by the three successors to Soviet leader Leonid Brezhnev, who signed the document with Carter.

Reagan has declined to say whether the United States will continue its policy of not undercutting the SALT II treaty limits when a new Trident nuclear-missile submarine comes into service late this year. To maintain the limits, the administration would have to compensate for this addition by destroying older weapons.

Carter, who was in Washington on a promotion tour for his new book about the Middle East, covered a wide range of subjects in the interview with The Washington Post and in a breakfast meeting with a group of Washington journalists.

Among other things, he said:

* Reagan's Strategic Defense Initiative (SDI) for a space-based missile defense, added to the already complex business of U.S.-Soviet arms control negotiations, creates an "almost insuperable" obstacle to an agreement.

* The United States should encourage movement in the Middle East peace process by the diplomatic intervention of Reagan, Secretary of State George P. Shultz or a high-prestige figure such as former president Gerald R. Ford or former secretary of state Henry A. Kissinger. Any lesser figure would be ignored by the contentious parties in the region.

* The time has come for the United States to explore the peace process with Palestinians, including Palestine Liberation Organization adherents who may be part of a Jordanian delegation in Middle East peace talks. Carter said this could be done while maintaining the letter of the 1975 U.S. pledge to Israel not to negotiate with or recognize the PLO until it changes its policy toward the Jewish state.

* One of the factors behind his campaign pledge and presidential decision to withdraw U.S. ground forces from South Korea was a public opinion poll indicating that only about 15 percent of the U.S. public supported the use of U.S. troops to defend South Korea.

Carter evidently referred to a Harris poll conducted in December 1974 for the Chicago Council on Foreign Relations. It reported that 14 percent of those responding favored U.S. military involvement if North Korea should attack South Korea, while 65 percent opposed U.S. involvement. About 40,000 U.S. troops were stationed in South Korea at the time.

"A slow, methodical . . . easing out and reducing of American forces" in South Korea would still be "the right thing to do," Carter said. He said he has "never comprehended fully" a 1979 U.S. intelligence estimate that North Korean troop strength was much greater than previously projected, a report that caused Carter to suspend his troop withdrawal program.

* Carter did not see the revolution that overthrew Nicaraguan President Anastasio Somoza in July 1979 as "a communist revolution" and his administration worked hard "to bring the new Nicaraguan government into the democratic circle . . .not to drive them into the camp of Moscow."

While saying the situation could be different today if his more conciliatory approach had been followed, Carter said "there's been a great exaggeration, primarily from President Reagan" about Nicaragua's political alignment. "It's not a communist nation. It probably has as much free enterprise, private ownership as exists in Great Britain," he said.

* The Democratic Party will regain control of the Senate in the 1986 congressional elections and has a good chance to regain the presidency in 1988 with a middle-of-the-road candidate and philosophy. Carter said he recommends economic conservatism, including reductions in the federal deficit, deregulation of industry and defense budget growth of 2 to 3 percent yearly, in a mixture with liberal ideas such as human rights, civil rights, environmental efforts and arms control.

While saying "I have nothing but friendship" toward Sen. Edward M. Kennedy (D-Mass.), Carter said he does not believe that Kennedy "would have an easy time" adopting a conservative image.

Carter recently said on the television program "60 Minutes" that he did not believe that Kennedy "would ever be approved" by the American people as a potential president.