The United States and the Soviet Union have agreed on a series of preparatory meetings that could produce a second summit meeting, including a Sept. 19-20 visit to Washington by Soviet Foreign Minister Eduard Shevardnadze, administration officials said yesterday.

President Reagan, reflecting optimism about U.S.-Soviet discussions completed here Monday, said in a White House speech that the series of meetings "could lead to a productive summit later this year." A White House official went further, saying the meeting between Reagan and Soviet leader Mikhail Gorbachev probably will be held in December but could occur as early as mid-November.

Despite indications of procedural progress, administration officials cautioned that substantive obstacles remain to a new U.S.-Soviet nuclear arms pact and that no agreement has yet been reached to actually hold a summit.

"Our arms reduction negotiations with the Soviet Union will not succeed overnight -- they will certainly be a long, arduous process," the president said in a speech to White House interns. "For the first time, however, we are not only pointed in the right direction -- toward reduction and eventual elimination of nuclear weapons -- we have begun to move down that road."

In his speech, Reagan reiterated his commitment to the Strategic Defense Initiative, the research program he hopes will lead to a missile defense that could be deployed in the next decade, but omitted his usual warning that SDI should not be used as "a bargaining chip." Instead, he said that "we won't bargain away" SDI, and that "we must continue our SDI program on schedule," though there is no firm schedule for it now.

Sources said that in a reply to a Gorbachev letter last week Reagan proposed holding off deployment of a missile system for seven years if the Soviets would accept eventual deployment and agree to cut the nuclear arsenals of the superpowers by 50 percent.

Administration officials have conceded that it would be unlikely that a system could be deployed for at least a decade. They have described as "negotiating positions" both Reagan's reply and Gorbachev's original letter calling for guarantees that no defensive system would be deployed for 15 to 20 years. Reagan said yesterday that "now the ball is in the Soviet court."

Suggestions that the two sides prepare for another summit through step-by-step discussions were brought to Washington late last week by Soviet Deputy Foreign Minister Alexander Bessmertnykh and provided the framework for three days of State Department talks covering nearly all U.S.-Soviet issues, according to U.S. officials.

Until recently, Soviet officials had emphasized the need for progress on particular issues -- such as intermediate-range missiles and nuclear testing -- as necessary steps toward the next summit. A few weeks ago they began giving greater emphasis to procedural steps to prepare for a summit, thus seeming to lessen the requirement for a guarantee of particular substantive accomplishments, in the view of U.S. officials.

In a reference to the procedural progress, Reagan said he had "agreed to the Soviets' suggestion of a work plan, involving a series of preparatory meetings that could lead to a productive summit later this year."

The "work plan" is reported to involve use of a variety of channels for a systematic review of the pledges made by the two leaders at the last summit in Geneva and of outstanding questions between the two nations.

A series of U.S.-Soviet meetings on regional issues has been held in recent months and a session on Afghanistan is planned for September. A meeting on nuclear nonproliferation issues was recently completed. Sessions on various arms control questions, including nuclear testing issues and compliance with earlier agreements, were started last week.

The next round of the major U.S.-Soviet talks on nuclear and space arms is scheduled to begin in Geneva Sept. 18. The exchange of letters between Reagan and Gorbachev is expected to establish the framework for those discussions.

Shevardnadze's visit to Washington will include meetings with Secretary of State George P. Shultz and Reagan, officials indicated. U.S. sources said the Shevardnadze visit here was agreed upon during the Bessmertnykh discussions and that official announcements from the two capitals are expected soon.