Secretary of State George P. Shultz and Soviet Foreign Minister Eduard Shevardnadze are expected to meet Friday in New York to continue U.S.-Soviet discussions in advance of next month's summit meeting, State Department officials said yesterday.

The meeting, which would come four weeks after Shevardnadze's discussions here with President Reagan and Shultz, was facilitated by the Kremlin's decision to name Shevardnadze as Soviet representative to the United Nations' 40th anniversary observance next week.

Earlier, it had been thought the Soviet Union would be represented by its longtime foreign minister, now president, Andrei A. Gromyko.

State Department sources said Shultz is expected to confer with Shevardnadze on the Soviet-American issues likely to be discussed at the summit meeting of Reagan and Soviet leader Mikhail Gorbachev in Geneva Nov. 19 and 20.

Since Shevardnadze was here, the Soviet Union formally has presented an arms proposal in Geneva covering strategic, intermediate-range and space arms.

The Reagan administration, meanwhile, has adopted a new interpretation of its legal obligations under the 1972 U.S.-Soviet Anti-Ballistic Missile Treaty.

Working-level U.S. and Soviet officials spent four days this week seeking to negotiate a new civil-aviation agreement between the two nations, but the State Department said late yesterday that the talks ended without agreement.

A State Department spokesman said "considerable differences on the economic basis on which service would be established" had been encountered. Other officials said it was the firm U.S. position to hold out for workable economic arrangements for Pan American World Airways and other U.S. carriers that might serve Moscow.

No date has been scheduled for resumption of the aviation talks, the State Department said.

Another set of U.S.-Soviet talks is scheduled here early next week.

It is to be an exchange of views on regional issues in Central America, the Caribbean and other parts of Latin America. Assistant Secretary of State Elliot Abrams will head the U.S. team.