In "an open letter to the people of Europe," President Reagan has offered to meet with Soviet leader Yuri V. Andropov "wherever and whenever he wants in order to sign an agreement banning U.S. and Soviet intermediate-range, land-based nuclear missile weapons from the face of the earth."

Vice President Bush unexpectedly read the letter at the end of a televised dinner speech here tonight, and the 600 invited guests, including West German Chancellor Helmut Kohl, rose in applause.

Praising Reagan's letter as "a testimony of the desire for peace of our American friends," Kohl said he thought he could speak for a majority of West Germans and many in East Germany in hoping that Reagan's offer will find "an open ear and outstretched hand" in Moscow.

The Soviet Union has flatly dismissed Reagan's "zero-zero" plan, which he proposed in November, 1981, for banishing medium-range nuclear missiles on both sides in Europe. With his letter, Reagan is again inviting Andropov to sign something he has rejected.

But the dramatic revelation here of Reagan's letter and Bush's visit to six NATO countries, a trip that began today, are part of a major new U.S. effort to seize the initiative from the Soviets in the battle for public opinion in western Europe.

NATO officials say they believe Andropov has been skillfully playing on fears about 572 new U.S. missiles to be deployed in western Europe to balance about 600 Soviet missiles already in place.

Western officials say they believe Moscow still hopes to halt deployment of the U.S. missiles through pressure of public opinion rather than through a negotiated agreement.

Reagan's letter did not suggest a full-scale summit meeting with Andropov. But Bush, answering reporters' questions through his press secretary, suggested that discussion of missile reductions would not rule out other matters if a summit were arranged eventually.

Kohl has been a leading advocate of a summit between Reagan and Andropov, on the theory that any contact between the two leaders should increase stability and avoid dangerous misunderstandings. Kohl repeated this earlier today when he met with Bush during the vice president's stop in Bonn, the West German capital.

Noting that nuclear arms negotiations have just resumed in Geneva, Reagan said in his letter that the United States "will continue to urge" that the Soviet Union dismantle its existing missiles aimed at western Europe. Reagan stuck to his pledge to deploy the new U.S. Pershing II and cruise missiles to counter the Soviet force unless an agreement can be reached with the Soviets.

"The Soviet insistence on maintaining a nuclear threat to America's allies while denying them the corresponding means to deter that threat remains the principal obstacle," he said. "A way must be found to overcome this obstacle. Just as our allies can count on the United States to defend Europe at all cost, you can count on us to spare no effort to reach a fair and meaningful agreement that will reduce the Soviet nuclear threat.

"In this spirit, I have asked Vice President Bush, in the city where East meets West a reference to this divided former capital of pre-war Germany , to propose to Soviet General Secretary Andropov that he and I meet wherever and whenever he wants in order to sign an agreement banning U.S. and Soviet intermediate-range land-based nuclear missile weapons from the face of the earth.

"I make this offer," Reagan said, "out of a conviction that such an agreement would serve the interests of both sides and, most importantly, that the people of Europe want nothing more. I urge Mr. Andropov to accept it."

While Reagan's letter continued to focus on his zero-option proposal, diplomatic discussion among the NATO allies has moved to possible compromises between Reagan's proposal and the most recent Soviet offer. Andropov has offered to reduce the number of missiles based in the European part of the Soviet Union to 162, which would equal the British and French nuclear missile arsenals.

There are many unanswered questions about Andropov's proposal, which has not officially been put on the Geneva bargaining table and which has been called unacceptable by the United States. Kohl, who has been among Reagan's staunchest supporters on this issue, today publicly reaffirmed his view that "the elimination of all land-based missiles" would be best.

West German officials said, however, that Kohl asked Bush to make certain that Washington carefully considers all Soviet proposals on their merits.

Kohl did not recommend any specific compromise, the officials said, but did stress to Bush that Washington should stick to its demands that any settlement allow equal nuclear forces on both sides. His conservative West German government, Kohl reportedly said, would never accept a situation in which NATO had no such missiles while the Soviets still had some of theirs.

Kohl also said he believes the United States should retain a mixture of Pershing II ballistic missiles and the slower moving, jet-powered cruise missiles in any force that may have to be deployed. The Soviets have appeared most determined to stop NATO deployment of the Pershings, which could strike targets inside the Soviet Union within eight minutes of launch from West Germany if they performed as advertised.

The Soviets, who maintain there is already parity in nuclear striking power in Europe, view the Pershing as a first-strike weapon and argue that the U.S. missiles would fundamentally change the balance of power because they could reach the Soviet Union while Soviet medium-range weapons cannot reach the United States.

In stops today here and in Bonn on a trip taking him to the Hague and then to Brussels, Geneva, Rome, the Vatican, Paris and London, Bush is trying to sell the U.S. position in the Geneva negotiations and to convince people that Reagan is sincere about arms control.

But he does not want to be seen as interfering in a crucial West German election on March 6, which pits Kohl against a Social Democratic challenger who has asked Washington to be more responsive to Andropov's proposals.

NATO officials continue to say they don't expect any shift in the U.S. position before the West German elections. But much will depend on what Bush hears in confidence from western European leaders. Most of them have pointed out that the zero option was not meant as a take-it-or-leave-it demand. Even Reagan has recently urged the Soviets to offer more "serious" proposals and said he was willing to negotiate.

In his speech tonight, Bush sought to attack "myths" he said are being used to undermine the U.S. position. He pointed out that the Soviets claim there was nuclear parity in 1977 and since then have added hundreds of new missiles while still claiming there is parity.

He said the new U.S. weapons are meant to preserve the American nuclear umbrella protecting Europe since the end of World War II. Bush said the new missiles would not be part of a strategy to fight a nuclear war in Europe but would enhance the ability to deter it from starting.