President Reagan concluded a grueling 10-day trip to Europe today with an offer to the Soviet Union to exchange additional missile launch information and improve the Washington-Moscow hot line in an attempt to "further reduce the risk of a nuclear conflict."

Capping a journey that included two summit meetings, a conversation with the pope and speeches to members of the British and West German parliaments, Reagan advanced the plan--which will formally be presented during nuclear reduction talks in Geneva beginning June 29--in a speech to a crowd of 20,000 on the grounds of the historic Charlottenburg Palace.

Reagan returned to Andrews Air Force Base at about 6:30 p.m. EDT Friday. He told a crowd, estimated at about 15,000, that his conferences had been arduous but successful. See Page A10

Reagan's offer to the Soviet leadership today is part of a package State Department officials call "confidence-building measures" that the administration hopes will reduce the risk of a nuclear war through accidental misunderstanding. Reagan has already proposed eliminating all medium-range nuclear missiles in Europe and beginning negotiations on reducing U.S. and Soviet strategic, or long-range, nuclear arms.

"It is time we went further to avert the risk of war through accident or misunderstanding," Reagan said today. "We shortly will approach the Soviet Union with proposals in such areas as notification of strategic exercises, of missile launches and expanded exchange of strategic forces data. Taken together, these steps would represent a qualitative improvement in the nuclear environment. They would help reduce the chance of misinterpretation in the case of exercises and test launches."

Reagan said he was considering unspecified "additional measures" as well.

An administration official, not speaking for attribution, gave these examples of what Reagan has in mind:

Expanding the existing notification to the other country of missile tests. Currently, this notification occurs only when projectiles leave the country of origin. Since the Soviets do much of their testing over their own country, there is no notification of many of their launches.

Transforming the "hot line" from what is a teletype connection into a direct line allowing voice communications.

Exchanging more data on the capabilities of strategic weapons so that each side is not forced to plan a "worst-case" scenario.

Banning certain low trajectory missiles, which are extremely difficult to detect and are therefore considered to be destabilizing.

It was unclear what the Soviet response would be to the offer. A ban on low trajectory missiles was proposed by members of Congress earlier but turned down by the Carter administration. In the second strategic arms limitation treaty both sides agreed to exchange data on the size but not the capabilities of strategic weapons.

The 71-year-old president, whose advisers acknowledged was severely tired by the trip, appeared to be in a subdued mood today. The crowd also was quiet, applauding most enthusiastically when Reagan promised to protect the independence and integrity of West Berlin.

"And let there be no doubt: The United States will continue to honor its commitment to Berlin," Reagan said. "Our forces will remain here as long as necessary to preserve the peace and protect the freedom of the people of Berlin."

Without quoting them, Reagan recalled the late president John F. Kennedy's words when he visited West Berlin in June 1962 and said, "Ich bin ein Berliner (I am a Berliner)."

"I can only add that we in America and the West are still Berliners, too, and always will be," Reagan said. "And I am proud to say today that it is good to be home again."

Earlier in the day, Reagan spoke to soldiers and their dependents at Tegel Airport and briefly toured the Berlin Wall.

"If I had only one message to urge on the leaders of the Soviet Bloc it would be this: 'Think of your own coming generations,' " Reagan said. " . . . . Do the Soviet leaders want to be remembered for a prison wall, ranged with barbed wire and armed guards whose weapons are aimed at innocent civilians--their own civilians?"

"Or, do they want to be remembered for having taken up our offer to use Berlin as a starting point for true efforts to reduce the human and political divisions which are the ultimate cause of every war?" the president added.

In many ways, the president's final day in Europe was vintage Reagan, summarizing the varied messages he has conveyed on his first presidential trip outside the continent as well as numerous themes from his political campaigns.

On the one hand, Reagan held out what appeared to be an olive branch. On the other, he described the Soviet system in harsh terms and repeated his frequent accusation that, "instead of working with the West to reduce tensions and erase the danger of war, the Soviet Union has engaged in the greatest military buildup in the history of the world."

At Tegel, Reagan spoke of a World War II B17 pilot who stayed with his plane when it was hit to comfort a wounded gunner rather than bail out. The pilot died and received the Congressional Medal of Honor posthumously.

Reagan said he had read the citation for this act of bravery "when I was serving in the same war," a reference to his World War II service in Hollywood making training films. He contrasted this account with a description of how the Soviets had given a gold medal to the man who had killed Russian revolutionary Leon Trotsky after he had fled from Stalin.

"They gave their highest honor for murder," Reagan said. "We gave our highest honor to a man who had sacrificed his life to comfort a boy who had to die."