The United States has proposed to the Soviet Union that the superpowers exchange inspectors who would count each other's weapons and monitor production and assembly plants as part of an on-site inspection plan for verifying future limits on intermediate-range missiles, administration officials said yesterday.

Details of the unusually ambitious and intrusive on-site monitoring, proposed by the United States as part of an intermediate-range nuclear force (INF) treaty, became known as President Reagan announced he has invited Soviet scientists to observe and possibly measure a U.S. underground nuclear weapons test in Nevada next month.

Reagan's offer yesterday was a renewal of earlier offers to the Soviets to monitor a U.S. test, which the Soviets previously refused to discuss. The president said his new message to Soviet leader Mikhail Gorbachev included information on a new on-site device to measure the yield of underground nuclear tests.

Reagan said that if agreement can be reached on an effective, on-site method for verifying the explosive power of future underground tests, he would "be prepared to move forward" toward ratifying the 1974 Threshold Test Ban Treaty and the 1976 Peaceful Nuclear Explosions Treaty.

These treaties were negotiated with the Soviets by the Nixon and Ford administrations, but have never been ratified.

A White House spokesman said he "believes" that no U.S. nuclear test will take place before the third week in April, which is the date Reagan specified in his invitation to Soviet observers. On Thursday Gorbachev said the Soviets will continue to observe a self-imposed halt to nuclear tests until the United States detonates its first explosion.

The new U.S. proposals on verification in both the INF and nuclear test areas would require more extensive cooperation for purposes of verification than the Soviet Union has been willing to grant. A Pentagon official said this was needed because of the belief that the Soviets in the past have cheated on arms-control agreements.

The verification plan for a new agreement on intermediate-range missiles was presented to Soviet negotiators shortly before the end of the most recent round of Geneva arms talks March 4, according to administration sources.

The plan was drawn up in interagency discussions under guidance of the Arms Control and Disarmament Agency which began last December, after the Nov. 19-21 Geneva summit at which Reagan and Gorbachev pledged to work out "effective measures for verification of compliance" with the arms treaties under discussion.

The Soviet negotiators "were not tickled pink" by the extensive U.S. proposal, said an administration official familiar with the Geneva talks. He added that the Soviets were "caught in a bind" because Gorbachev has said repeatedly in recent statements that the Soviet Union is prepared to go beyond spy satellites to on-site means of verifying arms agreements.

As presented to the Soviets in Geneva -- and explained by officials yesterday in Washington -- the U.S. plan for verifying an INF treaty involves:

*A "baseline count" of each side's intermediate-range missiles, including the Soviet SS20s and U.S. Pershing II and ground-launched cruise missiles, by inspectors of the other. This would formally establish current totals as a basis for agreed reductions.

*"Designated deployment areas," which might include hundreds of square miles or more. These would be the only areas where deployment of the INF missiles would be permitted during the three-year period which the United States has proposed for phased but complete elimination of this class of nuclear weapons.

*At "designated facilities" where weapons are made and assembled, a combination of human inspectors, electronic devices and spy satellites would monitor the weapons being produced. An official said that a U.S. inspector would not necessarily have to be on duty full-time inside a Soviet plant, but might be stationed "on the perimeter" to count Soviet weapons going in and out.

*Agreed procedures to monitor destruction of INF missiles as required by an accord calling for their elimination.

An official said the U.S. plan would also require a ban on the encoding of Soviet and U.S. radio signals from all missile tests, or telemetry. This would go further than either side has proposed in the past.

The system for measuring the yield of underground nuclear explosions that Reagan offered to the Soviets yesterday, called Corrtex, is already being used to measure the yields of tests by Los Alamos National Laboratory, which developed it.

It is based on the use of a cable placed down a hole at the site of the underground test. The explosion creates a "hydrodynamic" shock wave that the cable picks up. It provides a precise estimate of the size of the explosion, according to U.S. scientists.

A knowledgeable U.S. scientist said recently that the Corrtex system would not "intrude" on the Soviet test shaft and thus U.S. monitors would not be able to observe any Soviet test equipment or gather details of the explosion other than its yield. It would require only a few U.S. technicians, officials added.