President Reagan announced yesterday that he and Soviet leader Mikhail Gorbachev will hold a long-awaited summit meeting in Washington starting Dec. 7 to sign a treaty banning medium- and shorter-range nuclear missiles and work toward a pact next year that would halve U.S. and Soviet strategic offensive nuclear arsenals.

U.S. officials said the summit is tentatively planned for three days, but that the Soviets have asked for flexibility in case Gorbachev decides to stay longer. Shultz said the summit will be "basically in Washington" because Gorbachev does not feel he can take the extra time required for a cross-country tour of the United States.

A joint statement released in both capitals said the two leaders "envision" a return summit of Reagan to Moscow in the first half of 1988 and hope that a strategic arms treaty can be signed at that time.

The announcement was greeted cautiously in Congress, where Senate Majority Leader Robert C. Byrd (D-W.Va.) predicted "some problems with verification of the treaty" and Senate Minority Leader Robert J. Dole (R-Kan.) said the summit should be approached "with our eyes open, our expectations in check and our feet firmly on the ground."

Reagan announced the summit in the presence of Soviet Foreign Minister Eduard Shevardnadze, who arrived here early yesterday morning with a letter from Gorbachev proposing dates and an agenda.

Just one week earlier, Gorbachev declined to set dates for the meeting, telling Secretary of State George P. Shultz in a Kremlin session last Friday that he did not "feel comfortable" in agreeing to come to Washington without assurances of major strides toward curbs on strategic defense.

Amid reports of political disputes in Moscow which might have contributed to Gorbachev's hesitancy last week, Reagan went out of his way to describe the Gorbachev letter as "forthcoming and statesmanlike."

Shevardnadze, replying to a shouted question at the White House, denied there had been a Soviet "flip-flop" on setting a summit date and declared, "Everything is going on according to plans." At a news conference later, Shevardnadze maintained that "progress on the concept and agenda" for the summit since last Friday made yesterday's agreement possible.

The Soviet foreign minister, a member of the ruling Politburo, denied reports that disputes within ruling circles had affected the summit planning. He conceded that "differences of view of course exist in the party on various problems" but said that there was "certainly no split" in the leadership last week.

Reagan, with Shevardnadze and Shultz looking on in the White House briefing room, said "I've made it clear . . . they've not rejected this, that there is no way that we can give up SDI {Strategic Defense Initiative}, which we believe is offering an opportunity for peace in the world."

Reagan suggested that Gorbachev would not hold up a strategic arms treaty in an effort to curb strategic defense, saying that such a curb "is no longer put down as a flat demand" by the Soviets as a required condition of the 50 percent cuts in strategic offensive arms that the two nations are seeking.

But Shultz, briefing reporters at the State Department later in the day, said that the Soviets "continue to talk about these subjects as linked" even though the two sides had made "a little bit of headway" on the issue in the discussions yesterday. Shultz said that Shevardnadze had introduced a new term of "strategic stability" to describe the relationship of offensive and defensive weapons systems and that this concept would be pursued in future negotiations.

Shevardnadze spoke to the issue by saying that strict observance of the 1972 Antiballistic Missile (ABM) Treaty over an agreed period of time is "the groundwork" for the 50 percent cuts in strategic arms. "This is the main guarantee of strategic stability," he said.

A joint statement issued by the two governments suggested the areas of potential negotiation on strategic defense, saying that in their Washington meeting Reagan and Gorbachev will thoroughly consider instructions to their Geneva negotiators "on the observance of and nonwithdrawal from the ABM Treaty for an agreed period."

Reagan told reporters flexibility about SDI deployment is a subject that "we've agreed to discuss" and that this might contribute to eventual agreement on strategic arms.

The Soviet Union has proposed a 10-year nonwithdrawal period from a strict interpretation of the 1972 treaty banning antimissile systems in space. The most recent U.S. proposal is for a seven-year nonwithdrawal period. On other key points, the two sides disagree on what testing would be permitted during the nonwithdrawal period and what would happen after that is over.

Large differences also remain on the nature and details of the proposed 50 percent cuts in strategic offensive arms, which would leave each side with 6,000 nuclear warheads. Verification of such an accord is expected to present major problems.

Reagan seemed to rule out an "agreement in principle" on main points of a future strategic arms accord, along the lines of the 1974 U.S.-Soviet agreement in principle in Vladivostok. The president said he believed neither nation "should settle for anything less" than signing a formal treaty.

A White House official said agreement on a strategic arms accord is "effectively linked" to Reagan's Moscow trip, suggesting that completion of a treaty or some major progress would be necessary for the visit to take place.

The intermediate-range nuclear forces (INF) treaty that Reagan and Gorbachev are to sign at the December summit was reported by Shultz earlier this week to be "98 percent complete." Conceding that there is still work to be finished in Geneva, Shultz told reporters after the Reagan announcement that "if it doesn't get done, Mr. Shevardnadze and I are going to get kicked in the rear end very hard by our leaders."

Later in the day, Shultz told reporters, "We will get that treaty done before the summit, you can be sure of that."

Shultz brushed aside a question about political opposition to the treaty from conservative Republicans. He said it was "a very good agreement" and that this would be recognized by its critics once they examine it.

But Rep. Jack Kemp (R-N.Y.), a presidential candidate who opposes the treaty, issued a statement sharply criticizing the verification provisions of the treaty, which Reagan yesterday called "the most comprehensive verification regime in history." Kemp said the summit "may fundamentally endanger the security of future generations," and another GOP presidential candidate, former secretary of state Alexander M. Haig Jr., said the INF treaty should not be signed until the Soviets agree to cuts in strategic arsenals.

Shevardnadze said the Soviet side had several times brought up the issue of INF treaty ratification because of "bitter experience" of the 1979 SALT II treaty and other U.S.-Soviet pacts which were signed by the executive branch but never ratified by the Senate. "No one in the administration can fully guarantee that the treaty will be ratified." he said, but added that as of now, ratification "looks quite possible."

The president, who has been troubled by problems ranging from the cancer surgery of Nancy Reagan to the stock market crash, seemed in a jaunty mood as he announced the summit and briefly fielded questions. Asked why the summit talks are to start on the 46th anniversary of the Japanese bombing of Pearl Harbor, the president said that after the Soviets had proposed the date, "I thought to myself wouldn't it be wonderful if Pearl Harbor Day would become superceded by the day that we began the path to peace and safety through disarmament?"

Reagan left in early afternoon for Phoenix, Ariz., where he will attend a memorial service today for the first lady's mother, Edith Luckett Davis.

The White House had made several alternative plans to take Gorbachev to various U.S. cities, if he wanted to visit them, and to Reagan's California ranch. An official said that Shultz's reference to a "basically Washington" summit leaves open the possibility of a visit to Williamsburg, Va.

Shevardnadze planned to leave Washington late last night, canceling plans for a meeting today with the Senate Foreign Relations Committee.