MONTEREY, CALIF., NOV. 4 -- NATO defense ministers yesterday gave the Reagan administration the strong support it sought for a new U.S.-Soviet agreement to eliminate medium-range and shorter-range nuclear missiles.

The administration wanted the endorsement to fend off conservative criticism of the agreement and rebut recent assertions by former secretary of state Alexander M. Haig Jr., a Republican presidential contender, that it is opposed by West European leaders.

The ministers from North Atlantic Treaty Organization nations, wrapping up three days of private consultations here on NATO's nuclear arsenal, said in a communique that "we welcome and fully support the agreement in principle" eliminating intermediate-range nuclear forces (INF) with a range between 300 and 3,500 miles.

Weinberger and other U.S. officials told the ministers they needed a strong NATO endorsement to ensure that the treaty will be ratified by the Senate after it is signed in Washington on Dec. 7 by President Reagan and Soviet leader Mikhail Gorbachev, as agreed last week.

Lord Carrington, NATO's secretary general, said in an interview that Haig was "not correct" when he said last week that West German Chancellor Helmut Kohl, British Prime Minister Margaret Thatcher and other European heads of state oppose the treaty.

A West German official said, however, that "some European defense officials have been privately critical of the "double-zero" agreement but they now have decided that the U.S.-Soviet treaty's political benefits outweigh their concerns about its impact on NATO's military posture.

Carrington acknowledged there were "German hesitations" and British "worries," but said these stemmed from uncertainty about possible follow-on negotiations covering short-range or battlefield nuclear forces not covered by the INF agreement.

Some German officials favor negotiated reductions in short-range weapons because they would likely be detonated on German soil in a war. But the United States and Britain oppose such negotiations out of concern that they would lead to the "denuclearization" of Western Europe.

A German official said Defense Minister Manfred Woerner was privately skeptical of follow-on negotiations, but was asked by Bonn to seek inclusion in the ministers' communique of a NATO declaration at Reykjavik, Iceland, in June that the Germans interpreted as supporting such negotiations.

In a decision described by several officials as a pointed rebuke of the German interpretation, the ministers omitted the declaration from their communique yesterday, leaving the issue of possible reductions in short-range forces to be resolved at future NATO meetings.

Similarly, no decisions were made at the meeting about new deployments by NATO of nuclear forces such as new battlefield missiles, aircraft or submarine-launched ballistic missiles.

No decision was made either about continuing deployments of the weapons covered by the INF agreement in the period between the December signing and its formal ratification by the Senate next year.

But several senior NATO officials said the allies probably would cease the deployments in December, despite U.S. desires that they continue.

A study group is expected to reach a decision on the issue later this year.