Vice President Mondale promised NATO leaders today that the Carter administration will increase its commitment to the defense of Western Europe despite the new President's pledge to economize on the Pentagon budget.

On the opening day of a round-the-world diplomatic mission, Mondale told the North Atlantic Council that "while we are going to find economies in the defense budget, it will not be reflected in cuts in NATO muscle."

Referring three times in his address to the danger from the "continuing growth in Soviet military power." The Vice President said the Carter administration will fulfill the "programmed increases in NATO contributions" next year and "do more" in future years if West Germany and other European countries expand their own contributions.

A NATO spokesman said Mondale's pledge brought "a noticeable sign of relief" from the representatives of the 13 NATO countries, who had viewed with anxiety Carter's campaign promise to trim $5 to $7 billion from American defense spending.

Neither Mondale nor his aides was prepared to put a specific figure on the increase in NATO support programmed into the Ford budget for fiscal 1978, but they indicated that the figure would be reaffirmed and made public when Carter submits his budget proposals to Congress next month.

American officials at NATO said the total budgeted cost in the current year for U.S. forces and support elements in Europe was $11.7 billion.

In a press conference concluding a full day of meeting with Belgian and Dutch officials, leaders of the European Economic Community and NATO, Mondale also:

Said it was "very likely" that President Carter will join other Allied leaders at a summit conference in "midyear" to discuss common economic and political strategies. European sources said the meeting would probably be held in London in May.

Said Secretary of State Cyrus Vance would announce new American initiatives to resolve in Cyprus conflict between Greece and Turkey in Washington on Tuesday.

Said the Carter administration would support steps to bring Spain into the NATO alliance when its government take such an initiative.

Said he had "no knowledge" of the future status of NATO commanding Gen. Alexander Haig, the former Nixon White House aide with whom he conferred today. Mondale said, "I have not talked to President Carter" about whether Haig would remain in his post.

Mondale's talk to the NATO Council was described as a significant statement by the new administration, expanding a pledge to "sustain and strengthen" the American commitment to Western Europe that Carter sent through former Secretary of State Henry A. Kissinger when the NATO foreign ministers met here soon after the American election.

In his speech to the NATO Council, Mondale said, "President Carter takes office at a time when we have moved from the rigid period of the Cold War into a period of expanded contact and greater potential for accomodation . . . It is imperative that we continue this dialogue."

"At the same time," he said, "the continuing growth in Soviet military power and the uncertainties that lie ahead with inevitable changes in Soviet leadership in the years to come . . . make us keenly aware of the need for the NATO alliance to modernize and improve its defenses."

In addition to guaranteeing what he called the "modest increases" in U.S. support of NATO next year, Mondale said "President Carter emphasized to me . . . that he is prepared to consider increased investment in NATO's defense" in future years if the allies "join with us . . . to the extent of their individual abilities."

NATO spokesman David Kyd, who described the "sigh of relief" that greeted Mondale's speech, said the Vice President singled out West Germany and Norway as examples of prosperous countries that should increase their NATO contributions. Others like Britain and The Netherlands are facing domestic pressure to reduce their defense spending.

In a crowded press conference attended by more than 100 reporters, Mondale said the administration was "talking about an increase in the combat effectiveness" of NATO and has "not contemplated" any expansion of the 300,000 U.S. troops now in Europe.

He pledged without qualification, that "we will not unilaterally withdraw troops from Europe," saying "we cannot accept reductions in NATO defense capabilities except through negotiations with the Warsaw Pact." Mondale promised the NATO allies they would be consulted more fully than in the past on those troop-reduction talks, as well as the Strategic Arms Limitation Talks between the United States and the Soviet Union.

The Vice President told reporters his promise of increased assistance to NATO was "entirely consistent" with the administration's plan to trim the Pentagon budget because "the proposal by President Carter was not to cut muscle but to cut waste."

Mondale's pledge to strengthen NATO forces came at a time of rising anxiety and debate about the readiness of the allied forces to meet a possible Soviet attack.

NATO has been discussing a $2.4 billion project to equip its forces with 27 radar-packed, early-warning Boeing 707s, which would give it better assurance against a surprise Soviet attack.

Without referring to the controversy over NATO's strength, Mondale warned against the "rhetoric of impotence."

"It is appropriate," he said, "that we have a proper concern and response" to the Soviet buildup, "but it is important that we not exaggerate the situation to the point that questions are raised either about the present credibility of the alliance or our capability to deal with that challenge."

From Brussels, Mondale flew tonight to Bonn, where he will confer Tuesday with West German Chancellor Helmut Schmidt. Before leaving Brussels, Mondale phoned Carter and reported on the day's events.