President Reagan, reporting on Moscow summit talks, said Friday that Kremlin leader Mikhail S. Gorbachev is "a serious man seeking serious reform" but that the Soviet Union still should be viewed with caution.

"Let us embrace honest change when it occurs; but let us also be wary. Let us stay strong," Reagan said in the address.The president also said the West must continue to speak out about human rights conditions in the Soviet Union. "In matter of state, unless the truth be spoken, it ceases to exist," he said.

Winding up a 10-day journey that included five days in the Soviet capital, Reagan gave his summit assessment in a speech before the Royal Institute of International Affairs at Guildhall, a center of civic government for more than 1,000 years.

The speech was a rhetorical highlight of the trip, offering encouragement for Gorbachev's campaigns of "perestroika" and "glasnost" while expressing cautious hope for "a new era in history."

At the Guildhall, Reagan passed along a corridor lined with the Lord Mayor Sir Greville Spratt's personal guard of pikemen and muskateers. He was preceded by ceremonial sword and mace bearers into the wood-paneled Great Hall where he delivered the speech.

After a farewell to U.S. Embassy families here, Reagan and his wife, Nancy, boarded Air Force One for the return to Washington, where a welcoming ceremony awaited them at Andrews Air Force Base.

Reagan's four days of talks with Gorbachev did not produce any breakthrough on a strategic arms reduction treaty, though both sides said some key differences had been narrowed. Nevertheless, the two leaders displayed a warm personal relationship.

Reagan said the Soviet Union is dominated now by talk of democratic reform, in the economy, in political institutions, and in religious, social and artistic life - "in short, giving individuals more freedom to run their own affairs, to control their own destinies."

"To those of us familiar with the post-war era, all of this is cause for shaking head in wonder," Reagan said, expressing amazement about an American president and a Soviet leader walking together in Red Square, as he and Gorbachev did, talking about "a growing personal friendship and meeting."

He said that episode was "a special moment in a week of special moments."

"My personal impression of Mr. Gorbachev is that he is a serious man seeking serious reform," Reagan said. "I pray that the hand of the Lord will be on the Soviet people."

He said the strategy of the West for dealing with the Soviets was "bearing fruit.

`Quite possibly, we are beginning to take down the barriers of the post-war era, quite possibly we are entering a new era in history, a time of lasting change in the Soviet Union," he said.

"We will have to see," the president said. "But if so, it is because of the steadfastness of the allies - the democracies - for more than 40 years, and especially in this decade."

Prime Minister Margaret Thatcher, speaking after Reagan, said, "We warmly congratulate you and General Secretary Gorbachev on a very successful summit, one which will influence the course of history for years to come."

She also thanked Reagan for pushing the human rights issue, saying, "your words in Moscow will have shone like a beacon of hope for all those wherever they are who are denied their basic freedoms."

Reagan suggested he would continue to speak out against human rights abuses in the Soviet Union and elsewhere.

"We have learned the first objective of the adversaries of freedom is to make free nations question their own faith in freedom, to make us think that adhering to our principles and speaking out against human rights abuses or foreign aggression is somehow an act of belligerence . . .

"In matters of state," he said, "unless the truth be spoken, it ceases to exist."

Despite the impasse on a START treaty, Reagan spoke optimistically about chances for getting an agreement.

"We made tangible progress toward the START treaty on strategic weapons," the president said. "Such a treaty, with all its implications, is, I believe, now within our grasp."

However, he said, there are other elements as important as arms negotations.

"As I never tire of saying, nations do not distrust each other because they are armed; they are armed because they distrust each other," Reagan said. "So equally important items on the agenda (n Moscow) dealt with critical issues, like regional conflicts, human rights and bilateral exchanges."

Despite some progress, American negotiators say the two sides made no progress on some of the thorniest areas of dispute: sea-launched cruise missiles and the longstanding difference over Reagan's Star Wars missile defense system.

In his speech, Reagan paid a special Thatcher, his close friend and ally, noting that she had been among the first to suggest the West could "do business" with Gorbachev.

"At this hour in history, prime minister, the entire world salutes you and your gallant people and gallant nation."

Underscoring the theme of human rights he trumpeted in the Soviet Union, Reagan said, "the best indicator of how much we care about freedom is what we say about freedom; it is in this sense, words truly are actions."