West European officials today warmly welcomed President Reagan's proposals for nuclear arms reductions as a fulfillment of European wishes and a solid confirmation of the president's interest in arms control.

But leaders of the European protest against the stationing of new U.S. nuclear missiles in Western Europe gave a mixed reaction to the president's speech, with some tending to discount its importance while remaining suspicious of U.S. negotiating intentions.

West German Chancellor Helmut Schmidt and British Prime Minister Margaret Thatcher, meeting in Bonn for bilateral consultations and facing growing domestic opposition to nuclear weapon modernization plans, used a joint press conference to applaud the content and tone of Reagan's speech -- particularly his offer to cancel the new U.S. missile deployment if the Soviet Union dismantles its new SS20s and older SS4s and SS5s.

The timing of the president's message, delivered several days before a visit by Soviet President Leonid Brezhnev here, effectively strengthens Schmidt's hands for the summit meeting.

The anti-missile movement and an extensive Soviet media campaign have helped to place the Reagan administration and its NATO allies in a public role of intransigence against a peace-making Brezhnev. Now, the West German leader will be in a good position to promote the U.S. initiative with the Soviet leader and, as Schmidt told reporters, "to answer his questions" about Reagan's offers.

Schmidt, whose government pressed the United States to include the so-called "zero option" in the starting package for the upcoming U.S.-Soviet negotiations, said the speech gave him "a very firm basis" from which to approach Brezhnev, who arrives in Bonn Sunday for several rounds of talks with top Bonn officials.

Thatcher called Reagan's speech "a most important initiative" that would "receive a warm welcome not only in political circles but in the hearts and minds of people across Europe." The British leader said she now hoped for "a positive response" from the Soviet Union, but cautioned that the negotiations ahead would not be easy. "We recognize there is a long way to go," she said.

Reagan's message was also welcomed by the foreign ministers of Italy, the Netherlands and Belgium, whose countries had endorsed the zero option.

In contrast with the satisfaction West European governments found in Reagan's initiative, however, the president's message gained mixed reactions from leaders of Europe's anti-missile protest groups, and in some cases was viewed with open suspicion.

"We expected such a move in the field of negotiations," said William Bartels, international secretary for the Dutch Interchurch Peace Council, which is helping to plan a major demonstration in Amsterdam this weekend. "Of course, we will be glad if the negotiations turn out successful. But we are afraid there is too much manipulation of terms like the 'zero option' at this stage."

Bartels said he doubted the Soviets would accept the U.S. terms for canceling the new NATO program since the Soviets -- somewhat justifiably, he said -- see the new U.S. missiles as upsetting the current balance of East-West nuclear forces more than the new SS20s. He added, however, that "the aim of arms reductions is something we all applaud."

In London, opposition Labor Party leader Michael Foot, a frequent advocate of disarmament, said Reagan's proposal created "a real chance of success" for U.S.-Soviet negotiations, Washington Post correspondent Leonard Downie Jr. reported.

The Campaign for Nuclear Disarmament, however, said that while it "welcomes" Reagan's announcement, "we are wary, and we will stick to our demands" of removing missiles based in Europe. The group accused Reagan of leaving out of the U.S. position nuclear weapons already based in Europe.

Despite the protest leaders' qualms, it was apparent that Reagan's clear and broad enunciations of his administration's policy on several points of main interest to West Europeans was a morale boost for the beleaguered governments on this side of the Atlantic. They sounded grateful.

"I would like to express my deep appreciation and my satisfaction about the speech of President Reagan," Schmidt said in English, adding that it showed Reagan to be "a man who deep in his heart is searching for peace and is willing to negotiate." Schmidt noted this is how he had been trying to portray the American president to West Germans and others since Reagan's election.

While it is good domestic politics for Schmidt to have openly claimed credit, as he did on German television last night, for helping to shape the U.S. negotiating position, it now becomes good alliance politics for him to avoid any hint of independent maneuvering as he appeals to the Soviets to be flexible.

Bonn officials say they intend to keep in close touch with U.S. officials during the Brezhnev visit, and have arranged daily briefings for the Americans.