The administration's drive to counter Cuban and Nicaraguan activity has entered a new phase of intense diplomatic activity, reportedly including a secret meeting two weeks ago between Secretary of State Alexander M. Haig Jr. and Cuban Vice President Carlos Rafael Rodriguez.

State Department sources here and Mexican government sources contacted by Washington Post special correspondent Marlise Simons were unusually reticent about the report in the Mexico City daily newspaper El Pais that a Haig-Rodriguez meeting took place Nov. 23 during Haig's visit to the Mexican capital.

The State Department officially refused to confirm or deny the report, and other sources said they would not comment on it in any way.

Haig charged during his address Friday to the general assembly of the Organization of American States on the Caribbean island of St. Lucia that Cuba, with Soviet support, "has embarked on a systematic campaign of increasing interference against its neighbors."

A senior State Department official who accompanied Haig to the Caribbean meeting said that in diplomatic contacts "we've told the Cubans very clearly what we know about what's happened" in their hemispheric activities.

Haig's three-day stay on rugged, lush St. Lucia included a 90-minute private meeting with Nicaraguan Foreign Minister Miguel D'Escoto devoted to U.S. charges of growing "totalitarianism" and "militarization" in Managua and Nicaraguan countercharges of "verbal terrorism" and "threats" from the United States.

Haig made clear in public and private his concern that growing Cuban and Soviet connections in Nicaragua are creating a new source of danger to U.S. interests and regional stability in the hemisphere, in essence threatening to turn the Central American nation into "another Cuba."

Nicaragua's response as expressed by D'Escoto is that it has been forced to take drastic measures, including a military buildup, in response to threats against it from a hostile United States.

Although the dialogue with Cuba and Nicaragua did not seem to be bearing fruit, Haig held out greater hope for discussions he launched last week with the other nations of the hemisphere.

By taking the U.S. case to the OAS and promising to follow up in a forthcoming series of bilateral and small group meetings with Latin American states, Haig appeared to be reorienting U.S. policy to political rather than military priorities.

Any joint action in the hemisphere would require extensive consultations with friendly states and thus a large-scale political effort. Given Latin sensibilities about "Yankee imperialism," the chances for such an effort could be set back by a continuation of open, if ambiguous, verbal threats in Washington of unilateral military action.

Haig, while never foreclosing the possibility that the United States would take unilateral military action in the hemisphere to protect its interests, was notably cautious, almost muted, in his public rhetoric on St. Lucia. He told the OAS assembly, quoting President Reagan, that "we have no plans to send combat troops to Central America."

This carefully worded declaration caused sighs of relief among Latin diplomats, but Haig refused to discuss what Washington might or might not do if "plans" change or a response other than "combat troops" seems required.

In its drive for regional support, the United States would have to convince other states in the area that Cuba and/or Nicaragua represent a serious threat to the states' well-being and stability. One effort to do so was the lengthy confidential report on Cuban "covert activities" in the hemisphere dispatched to U.S. diplomats Nov. 8 for presentation to political and governmental leaders.

That document reportedly is being prepared for release in the form of State Department testimony in Congress.

More likely to galvanize the Latins would be dramatic evidence of growing Soviet involvement, such as the supply of Mig fighters to Nicaragua that Haig and his aides have forecast.

Given all this, the chances appear slim for a negotiated rapprochement between the United States and Cuba or Nicaragua. Nevertheless, Washington must demonstrate to its potential regional partners that it is willing to explore such solutions.

This need appeared to be behind Haig's meeting with D'Escoto last Wednesday and the State Department's refusal yesterday to confirm or deny the report of a meeting with the Cuban vice president, whether or not such an event took place.