Vice President Bush appealed today to Denmark's Social Democrats to abandon their opposition to scheduled deployment of U.S. medium-range nuclear missiles in other European countries and permit the Danish government to meet its obligations to NATO.

In a meeting with party leaders Bush said he stressed that by "staying firm and staying together," NATO had the best chance of persuading the Soviet Union of the need for flexibility in arms talks. But the session apparently was unsuccesful. Social Democratic Party leader Anker Jorgensen announced in advance that he would not be moved by Bush's arguments.

The vice president, who is on a 10-day tour of eight European countries, said of the meeting, "Believe me, it was frank."

The Social Democrats and other left-wing Danish parties have repeatedly outvoted the country's conservative minority government and called for a delay by NATO in the scheduled deployment of U.S. missiles later this year. Parliament has also ordered the government to withhold further payments of Denmark's share of NATO's deployment costs for the missiles, which are not scheduled to be installed in Denmark. Britain, Italy, the Netherlands, West Germany and Belgium are the five NATO allies where deployment is set.

If Soviet and American arms negotiators in Geneva fail to reach agreement, 572 U.S.-built Pershing II and cruise missiles will be deployed starting in December under the terms of a NATO decision reached in 1979.

Denmark's center-right governing coalition has been in the awkward situation of explaining to other NATO governments at alliance gatherings why it is unable to support plans to install the missiles as previously agreed. But as if to prove Denmark's basic commitment to alliance strategy, Bush heard the most ringing endorsements of NATO and U.S. nuclear policy here that he is likely to find in his trip through northern Europe.

"The Danish people's support for NATO is as strong as ever," Prime Minister Poul Schluter insisted in a toast at a lavish banquet last night in the Kronberg Castle, legendary scene of Shakespeare's Hamlet.

With East-West relations at a generally low ebb, Schluter said, "My government feels we should do our utmost to secure the cohesion and the solidarity of the alliance."

By contrast, the Social Democrats maintain that their pressure on the United States for progress in the Geneva negotiations reflects widespread uneasiness here and elsewhere in northern Europe over a stepped-up arms race. "We will ask the U.S. to show great flexibility in the decisive disarmament negotiations," Jorgensen said in a Danish newspaper interview. "The more constructive the U.S. is in its approach to that, the better."

Bush, in what was billed as the major speech of his European tour, told the Danish Foreign Policy Society that Reagan administration flexibility on arms issues had been demonstrated in "negotiation after negotiation." He said that seeking real reductions in nuclear weapons "drives the presidency of Ronald Reagan."

The Social Democratic Party, Denmark's largest, has used the nuclear issue to harass the government, which has been increasing its support in public opinion polls because of improvements in the country's economy in the 10 months it has been in office. Moreover, the coalition's inability to prevail on foreign policy issues is a considerable embarrassment to Schluter in the international scene and limits the influence he would like to have on leaders in other smaller European countries.

Small groups of anti-NATO demonstrators greeted Bush at various stops in his 30-hour Danish visit, but there was no evidence of militant public concern over the arms problem of the kind that marred Bush's visit to West Germany at the start of the eight-nation tour. In Krefeld, West Germany, Bush's motorcade was pelted with rocks and bottles thrown by an angry crowd of anti-American demonstrators.

As elsewhere on this trip, Bush also defended U.S. policy in Central America. But on this issue he was criticized by the Social Democrats as well as by by the friendly Schluter government, although to a far lesser extent.

"American policy in Central America is unacceptable," Jorgensen told the newspaper Politiken, "and is an expression of a hopelessly antiquated way of thinking. I fear this will lead to a new Vietnam."

Bush's response is to emphasize that the preponderance of U.S. aid in Central American is economic. "We recognize that hunger, poverty and social ills lie at the heart of the region's unrest," he said.

But the vice president's main message is that the Reagan administration's goals of democracy in Central America and arms reductions in Europe--goals it shares with European Social Democrats--are being frustrated by the Soviet Union and its allies.

Bush later flew to Dublin for a 24-hour visit and was greeted by about 100 demonstrators who gathered outside of the U.S. Embassy, The Associated Press reported. The protesters carried placards saying "Peace, Not Bullets" and "U.S. out of Central America," and shouted "Coward" and "U.S. Shame" as the vice president arrived in his bulletproof limousine for a Fourth of July party.