President Reagan, arriving home last night to a star-spangled welcome from an estimated 15,000 well-wishers at Andrews Air Force Base, proclaimed his European trip a complete success and said the events of the past 10 days highlighted this country's role as a peacekeeper around the world.

"I can report that we accomplished what we set out to do," Reagan said a few moments after Air Force One touched down. "Our alliances have never been stronger. The powerful friendships among free nations shall endure.

"As I listened to our European friends, yes, we have our differences, but our values and objectives are the same."

The president was greeted with a festive, flag-waving, band-playing reception that he professed to find a "complete surprise."

The remark drew laughter from the crowd, which was carefully assembled by the White House, State Department and Republican National Committee. Color-coded invitations were issued to the diplomatic corps, and dozens of buses were rented to transport government workers to Andrews.

Thousands who were to attend the ceremony never made it, as a massive traffic jam brought Suitland Parkway to a virtual standstill during the afternoon rush hour.

Reagan opened by praising the House for passing a budget on Thursday. "When I brought the word of the budget passage to our allies, they were looking forward to this as much as I was," he said.

The president said that both the economic summit at Versailles, France, and the NATO meeting in Bonn had gone extremely well and served to cement this country's relations within the Western alliance.

"After visiting six major cities in Europe, one thing stands out clearly: America has a lot of friends," the president said. "Yes, there were demonstrations . . . , but I can tell you that in every city we visited the streets were lined with people, many of them waving American flags."

During his remarks, made on the base's main airstrip, Reagan touched briefly on the two major troublespots in the globe--the fighting in the Falkland Islands and in the Middle East.

He said that, at such times, nations look to the United States to preserve freedom and maintain peace. "This is not a burden that we sought but it is one we shall not shirk," he said.

Reagan was formally welcomed back from his 10-day journey by Vice President Bush, who likened the president's European trip to that of Apollo 11 and quoted the astronauts: "We came in peace for all mankind."

The bulk of Reagan's brief comments were upbeat and positive, but there was one backhanded slight aimed at the Soviet bloc. The president noted that during the NATO meeting the alliance welcomed Spain as its 16th member. "When have you ever heard of a nation voluntarily requesting to be a member of the Warsaw Pact?" he asked.

The mood on Air Force One was joyous as the president's entourage left Bonn. Deputy press secretary Larry Speakes said the president toasted his staff with champagne upon completion of "a very successful trip." Added counselor Edwin Meese III, "This trip eclipsed any expectations the president had."

The trip was the president's longest period abroad and his first to Europe since his inauguration.