HAVANA, JULY 23 -- Three Cubans trying to leave the country have sought asylum in the Swiss Embassy, diplomats said today, bringing to 25 the Cubans entering embassies.

Cuba has said it will not allow any of the asylum seekers to leave the country, adding that they must either surrender unconditionally or stay in the legations.

Swiss diplomats said the three men entered the embassy in the city's Miramar diplomatic district Sunday afternoon. They asked for Swiss government protection to be able to leave the country, the diplomats added.

A Swiss Foreign Ministry statement released in Bern said the three had entered the embassy "despite strong military and police protection from the local authorities." A ministry spokeswoman said the three would be allowed to stay only until the embassy received assurance they were not in danger.

The Swiss represent the United States in Cuba through a U.S. Interests Section, which is in the old American Embassy, separate from that of the Swiss. Cuban police stand guard outside the Interests Section. Police also have sealed off the Spanish, Canadian and West German embassies and the Italian ambassador's residence, which is housing four Cubans.

There were 18 Cubans at the Spanish Embassy. The mission doubled its security force today by deploying five more members of an elite Spanish police unit as Madrid and Havana stepped up efforts to defuse a week-old dispute over the asylum seekers.

The five reinforcements of the Spanish police Special Operations Group arrived in Havana Sunday night and joined four already protecting the embassy.

Spain and Cuba have been locked in a bitter quarrel over the 18 Cubans at the Spanish Embassy, nine seeking to leave the country who sought refuge last week and nine others who mysteriously broke in early Saturday despite a heavy Cuban police guard.

Spanish diplomats strongly suspect the nine newcomers, whom they describe as "fit, well-built young men," may not be genuine asylum seekers. They have cited contradictions in their stories.

Spanish Ambassador Arturo Serrano de Haro, who has been recalled for consultations by his government, held last-minute talks Sunday night with Cuban Deputy Foreign Minister Jose Viera before leaving for Madrid.

"There is a willingness to try every way to reach a mutually acceptable solution, which in our case would mean respect for certain principles," Fidel Sendagorda, charge d'affaires at the Spanish Embassy, told reporters. Spain has asked Cuba to allow the refugees to leave the country.

Sendagorda said the Cuban authorities had indicated they wanted to keep dialogue open with Madrid to resolve the dispute, which has included a sharp exchange of protests. It was encouraging that the Cuban authorities had provided visas without hesitation for the five extra Spanish policemen, he said.

Sendagorda said the Spanish police were keeping a close watch on the nine Cubans who entered the embassy Saturday night. They were being kept separate from the others.

Spanish diplomats fear the kind of incident that shook the Czechoslovak Embassy a week ago when seven Cubans, who also penetrated a police guard, fought with other refugees and held Czechoslovak diplomats hostage for several hours. All eventually surrendered.