A group of Cuban exiles yesterday said it has requested permission to land 7,500 supporters at the U.S. Navy base at Guantanamo Bay in an attempt to establish a revolutionary government on Cuban soil.

But even if it is denied permission, Cubans United, the exile group, vowed to continue with plans to land a flotilla of about 15 boats at the base within the next three or four days.

"We don't want to fight. But we're going to land," declared Wilfredo Navarro, the group's leader. "What can they do? Shoot us?"

The group, which claims to include "90 percent of the fighting Cubans" now living in the U.S., said it has sent telegrams requesting permission to land at Guantanamo to President Reagan, Secretary of Defense Caspar W. Weinberger, Navy Secretary John F. Lehman Jr. and the entire Florida congressional delegation.

It has yet to receive a reply.

The Navy has a longstanding rule against political activity on any base, and a spokesman yesterday said any civilian attempting to go to Guantanamo without the Navy's permission will be arrested or turned away.

The first boat carrying Cubans United supporters tried to leave Miami more than a week ago but was stopped for safety reasons by the U.S. Coast Guard, which claimed the boat was overloaded and didn't contain enough life jackets. After more life jackets were purchased, the boat left again but was delayed from reaching Cuba by tropical storm Dennis.

Last night, the Coast Guard said in Miami that the last of the Cuban vessels bound for Guantanamo ran aground in the British West Indies Sunday with no loss of life, Associated Press reported.

The Coast Guard said that two other Cuban vessels had turned back Sunday with engine trouble and that no others are at sea, AP reported.

Once at Guantanamo, Navarro said, the group wants to set up a camp outside the base. He claimed military officers and civilians, unhappy with Fidel Castro's Communist regime, would supply the group with weapons and logistic support and enable it to set up a revolutionary government.

Another purpose of the action will be to call attention to rumored U.S. plans to return the Guantanamo base back to the Cuban government. Asked if the publicity Cubans United hopes to generate would make the effort worthwhile even if the flotilla isn't allowed to land, Navarro replied, "Yes, 100 percent."