MARSAXLOKK BAY, Malta--President Bush and Soviet Leader Mikhail S. Gorbachev wrapped up two days of superpower summitry yesterday, claiming strides toward a new era of East-West peace but underscoring differences that linger at the end of a 45-year Cold War.

Both leaders said they would meet again next year in the United States, and expressed the hope--but not the certainty--they would be able to sign historic agreements in 1990 to cut long range nuclear weapons and conventional forces in Europe and make progress toward a chemical weapons ban.

"We stated, both of us, that the world leaves one epoch of Cold War and enters another epoch," Gorbachev said at an unprecedented joint news conference that marked the end of two days of storm-tossed talks held aboard a Soviet luxury liner. "We are just at the very beginning of our long road to a long-lasting peaceful period."

Said Bush after his first summit as president, "I am optimistic that as the West works patiently together and increasingly cooperates with the Soviet Union, we can realize a lasting peace and transform the East-West relationship into one of enduring cooperation."

Even so, neither president sought to gloss over differences on two topics, the Soviets' call for cuts in naval forces and American anger at the continued flow of Soviet weapons to leftist rebels in El Salvador.

The joint news conference in Malta was held aboard the Soviet luxury liner Maxim Gorky, which was pressed into service as the site for the two days of talks after bad weather forced cancellation of plans to use U.S. and Soviet warships anchored offshore. An afternoon session and a dinner on Saturday were cancelled because of the rough weather.

Bush and Gorbachev met for eight hours over two days during a time of extraordinary change in Eastern Europe. The upheaval was dramatized in the summit's final hours by the resignation of the East German leadership and the formation of a new government in Czechoslovakia that opposition leaders immediately denounced as too much like the old one.

Both leaders voiced optimism that ongoing arms negotiations could be wrapped up soon--although Gorbachev sounded slightly more upbeat.

The Soviet leader said he hoped that two treaties could be signed next year: one calling for sharp cuts in both sides' long-range nuclear missiles when he and Bush meet next June in Washington; and another for cutting troops in Europe by the end of next year.

Bush also applauded efforts by the Soviet Union to make its economy more market-oriented, saying "I would like to have a climate in which American businessmen can help in what Chairman Gorbachev is trying to do with reform."

The administration has promised to give Moscow most-favored-nation trade benefits, and to support its bid to participate in the General Agreement on Tariffs and Trade (GATT), an international trading organization, in exchange for Soviet relaxation of emigration restrictions on Soviet Jews.

About his face-to-face sessions with Gorbachev, Bush said afterwards: "You get the feeling he really wants to work with us and he knows that I'm cautious," Bush added. "...I'd like to think he thought I knew what I was talking about."

Gorbachev made fun of Bush's celebrated caution, in fact, telling the joint news conference, "In our position, the most dangerous thing is to exaggerate" the accomplishments of the Malta summit "and that we should always preserve elements of cautiousness--and I use the favorite word by President Bush."