MOSCOW (AP) _ Mikhail S. Gorbachev engaged President Reagan in a lighthearted battle of Russian proverbs at their summit reunion Sunday, and made pointed reference to Reagan's past enmity toward the Soviet Union.

At the start of Reagan's first visit to what he once called an ''evil empire,'' Gorbachev challenged his guest to learn more about the Soviet Union and its people.

''You, Mr. President, have traversed the great distance that lies between our two capitals to continue our political dialogue,'' the Soviet leader said in a welcoming speech. He noted that Reagan was finally visiting ''a country which you have so often mentioned in your public statements.''

Reagan said the steady improvement in U.S.-Soviet relations and more frequent meetings between superpower leaders was the result of patience. Then he reached for a Russian proverb to put his thoughts into words.

''Rodilsya, ne toropilsya (It was born, it wasn't rushed),'' Reagan said, reading from a notecard.

The president initiated the exchange of proverbs at his Washington summit meeting with Gorbachev in December, when he referred to the quandary of arms control negotiations. ''Doveryai, no proveryai (trust, but verify),'' he said.

Greeting Reagan on Sunday in the Kremlin's opulent St. George's Hall, Gorbachev took note of his guest's fondness for literary references.

''Aware of your interest in Russian proverbs, let me add another one to your collection,'' he said. ''It is better to see once than to hear a hundred times.''

Gorbachev's advice came after an oblique reference to Reagan's critical remarks in the past about the Soviet Union, which the president had never visited.

Reagan aroused the wrath of the Soviet media and government officials in 1983 when he told an American television audience that the Soviet Union was an ''evil empire.''

But Gorbachev and Reagan agreed Sunday that times have changed since their first summit in Geneva in November 1985.

''As we see it, long-held dislikes have been weakened; habitual stereotypes stemming from enemy images have been shaken loose,'' the Soviet leader said.

''Everyone can improve, even in later years,'' U.S. affairs expert Georgi A. Arbatov said on NBC-TV's ''Meet the Press'' program as he tried to explain why Reagan's views of the Soviet Union had changed.

On the eve of his arrival here, Reagan said in a Soviet television broadcast that he could not have conceived of visiting Moscow during the early years of his presidency.

''I think there is a difference between this general secretary and other leaders of your country that I've met with in the past,'' Reagan told the state-run broadcast service. ''No, I could not have foreseen your present leader.''