President Reagan yesterday sent a letter to Soviet leader Mikhail Gorbachev offering not to deploy a "Star Wars" missile defense for seven years in return for deep cuts in nuclear arsenals of both superpowers as well as Soviet acceptance of an eventual space-based missile defense, administration officials said.

Reagan's letter was a reply to a Soviet proposal in a June 23 letter from Gorbachev, which linked continued U.S. adherence to the 1972 Antiballistic Missile (ABM) Treaty for 15 to 20 years to reductions in strategic nuclear weapons.

White House chief of staff Donald T. Regan said the president is "hopeful that the arms control process would go forward" and said that Reagan anticipates a "favorable reply" from Gorbachev. Regan declined to discuss details of the reply on grounds that Gorbachev should have the chance to examine the letter before it is disclosed to the U.S. news media.

But other officials said the president had set forth "a negotiating position" that they said indicated a willingness to deal with Soviet concerns about the U.S. Strategic Defense Initiative (SDI), a research program that the president hopes will produce an antimissile system capable of protecting the nation from nuclear attack.

A U.S. official said the president is "flexible on the deployment question" but expressed U.S. intentions to continue research, development and testing of a defensive system to the extent permitted by the administration's interpretation of the ABM Treaty. The official said Reagan had made the point that the Soviets also were engaged in such research and wanted Soviet recognition of the "conceptual need" for such a system at an unspecified future time.

"The idea is to have a system that could be deployed if the Soviets did not reduce the number of missile warheads or engaged in a later buildup after reducing them," this official said.

Thus far, the Soviets have given no public indication that they are interested in an agreement that would allow for full development of a space-based defensive system such as SDI envisages. Recent Soviet statements have appeared more flexible than earlier ones by suggesting that the Soviets might tolerate research on some antimissile technologies, but the Soviets have consistently insisted that they will not accept full development of defensive systems that they consider banned by the ABM Treaty.

While Reagan is now proposing that a deployment of a missile defense system will not occur before 1993, Lt. Gen. James A. Abraham-son, the SDI director, said earlier this week that such a system could not be deployed for at least a decade. U.S. officials expect that the Soviets will respond with a counteroffer and that the issue will be negotiated at the next round of nuclear arms talks in Geneva in September and discussed at a second Reagan-Gorbachev summit later this year.

U.S. officials said Reagan also wanted deeper cuts in the number of nuclear warheads than the Soviets have proposed. Gorbachev had called for a 35 percent reduction in strategic nuclear arms; Reagan was said to have proposed a 50 percent reduction.

The Reagan reply also contained a U.S. response to Soviet proposals limiting medium-range missiles in Europe, but officials gave no details of the "compromise offer" they said the president had proposed.

Officials said Reagan's reply was "comprehensive" in the sense of dealing with a number of important issues but that it was not highly detailed on many of the most difficult questions. "It is a basis for negotiation, not any sort of take-it-or-leave-it proposal," an official said.

Summit preparations, including the status of arms control negotiations, are expected to be discussed Monday by Secretary of State George P. Shultz and Soviet Deputy Foreign Minister Alexander Bessmertnykh. The Soviet official, who has major responsibility for U.S. affairs, will be in Washington to conduct a broad review of U.S.-Soviet relations, according to State Department officials.

Officials expressed hope that the Shultz-Bessmertnykh meeting, the Reagan letter and other consultations under way will lead to meetings in Washington in September with Soviet Foreign Minister Eduard Shevardnadze. This in turn could be a major step toward scheduling a second summit between Reagan and Gorbachev, who met for the first time in Geneva last November.

A White House official said yesterday he anticipated that the second summit could be held in December. A State Department official said recently that a summit could be held either in mid-November or early December. Reagan has made it known he does not want a summit until after the mid-term elections on Nov. 4.

Staff writer Don Oberdorfer and researcher James Schwartz contributed to this report.