President Reagan and Soviet President Mikhail Gorbachev Saturday hailed the dramatic improvement in U.S.-Soviet relations in an exchange of televised and highly optimistic New Year's messages to the American and Soviet people.

"1988 is memorable for all of us as a year when we began reducing the most terrifying weapons _ nuclear weapons," Gorbachev said. "That alone is enough for it to go down in history as a landmark, a great turning point in world affairs."

Reagan said the two superpowers, despite differences, had been able to find "common ground" on the "vital issues of human rights, arms reductions, regional problems and bilateral relations." He said that because of U.S.-Soviet cooperation, the world was safer than it was a year ago, "and I pray it will be safer still a year from now."

The White House released the messages on a day when Reagan celebrated his final vacation as president by playing a round of golf with professionals Lee Trevino and Tom Watson on the private course of publisher Walter Annenberg and attending a New Year's Eve party at the Annenbergs' for the 20th consecutive year. Reagan also telephoned Canadian Prime Minister Brian Mulroney to congratulate him on the Canadian Parliament's approval of the U.S.-Canadian free trade agreement.

It was the fourth consecutive year that Reagan and Gorbachev had exchanged New Year's greetings.