The leaders of seven major industrialized democracies today endorsed postwar unity and the U.S. position at the Geneva nuclear arms talks, but the summit's first full working day also brought a series of troublesome challenges to the Reagan administration.

In their major political declaration of the two-day meeting, the seven countries underscored the 40 years of democracy and prosperity that have marked European society since the end of World War II. The unity theme, long sought by the summit host, West German Chancellor Helmut Kohl, was carried through to the joint statement of support for Washington's negotiators at the Geneva arms talks with the Soviet Union.

The unity gave way on three other key issues, however:

* Clear disapproval of President Reagan's decision to impose a trade embargo on Nicaragua broke into the open, with most participants expressing serious differences both with the principle of a trade embargo and what was said to be a lack of consultation.

* The summit participants pointedly avoided mention of Reagan's ambitious research program into space-based antimissile defense. Summit participants said the omission reflected recognition that they are far from reaching a consensus on Reagan's Strategic Defense Initiative, which they have been invited to join.

* Reagan's goal of winning summit endorsement for an early date to begin a new round of global trade talks appeared frustrated by French demands for a specific agenda in advance that would safeguard the interests of European farmers.

As the summit approached its conclusion, the White House announced details of Reagan's controversial plan to lay a wreath with Kohl at a German military cemetery in Bitburg Sunday. Officials said the cemetery appearance would take 10 minutes and would follow a 50-minute visit, including a speech, at the Bergen-Belsen concentration camp site.

West German sources said the West German government pushed for a strong endorsement of the U.S. stance in Geneva, partly to compensate for the political travail Reagan has suffered because of his planned appearance at Bitburg. But the controversy continued to simmer today.

Relatives of anti-Nazi resistance fighters, who were invited by the government in Bonn to join Reagan and Kohl at the Bitburg ceremony, expressed some reluctance today about participating in the controversial visit. West German Col. Berthold von Stauffenberg, son of a German officer who tried to assassinate Hitler, said he found the ceremony distasteful but would attend out of his sense of military duty.

West German Jewish and Gypsy organizations, representing survivors of the Bergen-Belsen camp, announced that they would boycott Reagan's appearance at the concentration camp memorial because of their outrage about Reagan laying a wreath at the Bitburg cemetery, where 49 SS soldiers are buried.

At today's summit sessions, after Secretary of State George P. Shultz presented the U.S. rationale for imposing trade sanctions on Nicaragua, several foreign ministers flatly warned that the decision could prove counterproductive.

West German Foreign Minister Hans-Dietrich Genscher said "it is well known that European states do not tend toward embargo measures in any form." He stressed that sanctions failed to produce political change in Cuba or Poland and would not work in Nicaragua.

Britain's Geoffrey Howe and France's Roland Dumas warned that the trade embargo risked driving the Sandinistas even further into the Soviet camp. Canadian Foreign Minister Joe Clark complained that his government had not been notified, and he elicited assurances from Shultz that Canadian trade would not be affected by the sanctions.

While frustrated by France's refusal to go along with early trade talks, Reagan also faced a skeptical audience as he reported on U.S. efforts to reduce huge budget deficits. European leaders believe the deficit has fueled high interest rates, pulling badly needed investment capital out of their countries.

Reagan used a luncheon discussion of their economies to tell the other leaders that he would reduce U.S. budget deficits, but his senior aides were fending off questions all day about why Reagan has been losing budget votes in the Senate this week.

U.S. officials admitted that an allied consensus on the Strategic Defense Initiative could not be achieved at the summit. Recognizing the difficulties of gaining unanimous endorsement, they said the administration had not pressed the other governments for a joint statement of support.

Even though it was omitted from the political declaration, Reagan's proposal has been a frequent topic in bilateral and group summit meetings. A senior U.S. official said "it's far too early" to answer allied questions about financing the $26 billion space defense program.

Several allied countries that have expressed interest in joining the research program have been invited to Washington for detailed discussions about their possible role in the project, and U.S. officials said they did not want to risk a confrontation over the issue at the summit.

The Kohl government also did not want to spoil the summit with a fight over the missile defense system. There were indications today from U.S. officials that Kohl might mention Reagan's program in his summation at the close of the summit Saturday.

For months, Kohl has sought to use the summit for a ringing political declaration that would celebrate Bonn's post-World War II reconciliation with western allies and 40 years of democracy and prosperity. Today's joint declaration, reached after little debate, fulfilled Kohl's aims of demonstrating unity to counter a Soviet-led propaganda campaign accusing Bonn of expansionist designs.

The participants paid tribute to all those who lost their lives "by acts of war or as victims of inhumanity, repression and tyranny." But they also stressed that "the end of the war marked a new beginning" of partnership between former foes.

The summit leaders declared their support for the ultimate reunification of the divided lands of Germany and Korea, reportedly at the behest of the Bonn and Tokyo governments.

"We deplore the division of Europe," the leaders declared. "We look forward to a state of peace in Europe in which the German people will regain its unity through free self-determination . . .

"In Asia, we earnestly hope that a political environment will be created which permits the parties to overcome the division of the Korean peninsula in freedom."

In what U.S. officials described as the most pleasing outcome of the summit today, the participants added to their declaration an endorsement of the U.S. position in the Geneva arms negotiations after the fruitless first round of talks.

"We appreciate the positive proposals of the United States," they said. "We urge the Soviet Union to act positively and constructively in order to achieve significant agreements."

Reagan told the other leaders that he was "disappointed by the lack of any serious Soviet flexibility" in Geneva, a senior official said.

The official said the Soviets have "taken a linkage approach" in Geneva in which they are seeking to "hold progress in strategic arms and intermediate-range arms areas hostage to concessions by the United States in the space and defense area." He said, "We have told the Soviet Union in the negotiations that the approach is designed to produce paralysis."

Reagan is scheduled to meet Saturday with Italian Prime Minister Bettino Craxi, who is said to be carrying a letter from Soviet leader Mikhail Gorbachev. An Italian spokesman said the letter concerns "the Geneva arms control talks and Soviet preoccupations about the U.S. space defense project."

It is believed that Craxi's relatively positive response to Gorbachev's declared six-month moratorium on deployment of SS20 missiles in Europe induced Moscow to use him an intermediary.