UNITED NATIONS — Secretary of State James A. Baker III and Soviet Foreign Minister Eduard A. Shevardnadze reported "good progress" Friday toward completing a treaty this year slashing the superpowers' arsenals of long-range nuclear arms by more than one-third.

In a seven-hour meeting wrapped around the dedication of a bronze sculpture incorporating dismantled U.S. and Soviet intermediate-range missiles, Baker and Shevardnadze also cleared up the remaining technical issues of a treaty reducing conventional weaponry in Europe, which the two men settled in principle on Wednesday.

"We are a little tired, but the results are good," Shevardnadze said.

The meeting was the fourth that Baker and Shevardnadze have held in a little more than a week while the Soviet foreign minister has been in New York to attend the opening of the U.N. General Assembly.

Baker predicted that U.S. and Soviet arms control negotiators in Geneva will be able to complete work on the strategic arms limitation treaty in time for President Bush and Soviet President Mikhail S. Gorbachev to sign it at a summit meeting in Moscow before the end of this year. If that expectation is realized, it would be the third Bush-Gorbachev meeting this year following sessions in Washington and Helsinki, Finland.

The most difficult remaining issue, Baker said, is a provision intended to prevent the United States and the Soviet Union from trying to circumvent the purpose of the arms reduction pact by transferring strategic technology to allies not covered by the treaty. In practice, the issue affects only U.S. cooperation with Britain on advanced nuclear technology. The Soviet Union no longer has any allies that it would trust with such advanced weaponry.

In the past, the United States has refused to accept any limitations on its military relationship with London.

"Non-circumvention has not been fully completed, but we made some good progress on that," Baker said. "If we are able to do that, a number of other issues that are outstanding should fall into place."

He said there are remaining disputes concerning Soviet plans to modernize their giant SS-18 rockets and over the Soviet Backfire bomber. But he said those matters can be settled quickly once the non-circumvention issue is settled.