Secretary of State George P. Shultz left Washington last night after forecasting that he should be able to "wrap up" a treaty banning medium-range and shorter-range missiles when he reaches Moscow next week and set the date for a U.S.-Soviet summit meeting later this year.

"There's no major issue of principle that should prevent that," said Shultz, who qualified his optimism only by saying that the Soviets must continue to negotiate last-minute details in good faith and with a desire to finish the job.

Shultz was much more restrained in his description of prospects for movement in the Middle East peace process during the first five Mideast-related days of his overseas trip. To an even greater degree than his aides in the past few days, he seemed to lower expectations by describing his mission in that region as only to "touch base with our friends in the Middle East on a number of issues."

Regarding the treaty to ban intermediate-range missiles, Shultz said the work of arms negotiators in Geneva has been "strong . . . professional . . . rapid" since he and Soviet Foreign Minister Eduard Shevardnadze resolved the most difficult remaining issues in Washington a month ago.

Consequently, he said in a news conference several hours before his departure, "I hope I don't have to spend too much time" on wrapping up the treaty in Moscow.

"I'm getting tired of INF {intermediate-range nuclear forces}," said Shultz. "I want to get on to strategic arms," a reference to the intercontinental missiles and bombers identified by both sides as the likely focus of intensive discussion in the coming Moscow talks.

Shultz gave no indication of any change in the U.S. refusal to negotiate on Moscow's terms regarding the development of space weapons like those envisioned in President Reagan's Strategic Defense Initiative. While seeming to lower their sights in this area, the Soviets continue to insist that some limitations on defensive and space arms must be negotiated to permit large cuts in strategic offensive arms.

At the same time, though, Shultz did not close the door to possible future changes in the U.S. position if the Soviets make new proposals. In that case, he said, "I'll be very much interested."

Before arriving in Moscow next Thursday for two days of meetings, Shultz will meet leaders of Israel, Saudi Arabia, Egypt and Jordan in visits that begin with his arrival in Israel this afternoon. Shultz said that, while in Israel, he also hopes to meet a representative group of Palestinian leaders from the West Bank and to see Ida Nudel, a prominent Jewish activist who has just been permitted to emigrate from the Soviet Union.

Saudi Arabia and some others in the region have pressed Shultz to add Syria to his itinerary because of that nation's importance to the peace process. Shultz defended this omission from his schedule on grounds of lack of time. State Department officials said Assistant Secretary of State Richard W. Murphy might visit Damascus after Shultz leaves the area if developments warrant such a trip.

Shultz did not repeat the statements of aides that he is bringing "new ideas" about the peace process to his first Middle East mission in 29 months. He appeared to put most of the burden for immediate movement on his Mideast interlocutors, saying that "I will review these matters and see if they have any creative thoughts about how they might go further."

"I don't go there with any particular new thing," Shultz said.