ST. GEORGE'S, Grenada--Under a dazzling Caribbean sun, President Reagan yesterday retraced the steps of American invasion forces that ousted a radical Marxist government from this tiny island 27 months ago and vowed the United States also "must help those struggling for freedom in Nicaragua."

Reagan flew here to honor the 19 servicemen killed in three days of fighting that forced Cuban troops from Grenada and led to formation of a democratically elected government.

He laid a green wreath with a purple ribbon at the foot of a memorial to the 19, then stepped back and stood silent for a moment.

In a speech hours later to a cheering, flag-waving crowd, Reagan likened events in Nicaragua to those that prompted him to order the invasion of Grenada and declared he won't be satisfied "until all the people of the Americas have joined us in the warm sunshine of liberty and justice."

He was introduced as "our own national hero, our own rescuer" and the audience estimated at more than 20,000 roared approval when Reagan hailed democracy in Grenada and declared, "When people are free, their rights to speak and to pray are protected by law, and the goons are not running the jails, they are in the jails."

The President spoke on a stage emblazoned with a large green and yellow sign saying "Grenada Welcomes President Reagan." Small girls dressed in red, white and blue costumes danced with floral wreaths above their heads to welcome him to the outdoor cricket park.

While making no overt threats against Nicaragua, Reagan's statements--particularly coming on the site of the last open use of U.S. military forces--could hardly be construed as comforting to the leftist government 1,500 miles to the west.

Administration officials have said repeatedly they have no plans to invade Nicaragua, but they are making a concentrated effort to gain congressional support for $100 million in aid for rebel groups trying to overthrow the Sandinista regime in Managua.

Reporters with advance copies of Reagan's speech asked him before it was delivered whether he had any plans to use military force in Nicaragua.

"No," he replied. "I think it's an entirely different situation. We have no plans."

But in his speech, Reagan said: "Today in Nicaragua we see a chain of events similar to what happened here. We hear the same excuses made for the communists, while the people of Nicaragua see their freedom slowly but surely eaten away."

The President said, "We won't be satisfied until all the people of the Americas have joined us in the warm sunshine of liberty and justice."

Crowds cheered Reagan's motorcade as it wound through the hilly, lush countryside in 82-degree weather. Women waved bouquets of flowers and danced as Reagan passed.

During a visit of barely five hours, Reagan met with the island's governor, Paul Scoon, and with prime ministers of nine English-speaking democracies in the eastern Caribbean.

Posing for a picture with the prime ministers on the steps of the governor's mansion, Reagan was asked if he felt like a hero for having preserved democracy in Grenada.

"Don't embarrass me," he replied. "I didn't fire a shot."

Nonetheless, Grenada's prime minister, Herbert Blaize, declared a national holiday for Reagan's visit. He said the president did "the thing that helped us get out of a hole when we needed it most" by sending U.S. troops after Prime Minister Maurice Bishop was overthrown and assassinated.

On Oct. 25, 1983, a 6,000-member U.S. force invaded Grenada and removed a military junta that had seized power six days earlier. Reagan described it as a rescue mission for about 600 American students at St. George's University Medical School campus.

Air Force One landed at Point Saline International Airport, scene of some of the strongest resistance to the invading U.S. Army Rangers and Marines from Cuban soldiers and construction workers armed with automatic rifles. Twenty-four Cubans were killed in the fighting.

In his speech, Reagan portrayed Cuba as an international menace and said President Fidel Castro's "tyranny still weighs heavy on the shoulders of his people and threatens the peace and freedom of the hemisphere."

Reagan announced that U.S. funds for training and scholarship programs for the Caribbean will be increased threefold. In addition, he said a new program is being initiated to guarantee access to the U.S. market for Caribbean-produced clothing made from cloth woven and cut in the United States.

Reagan also said the tax bill pending in Congress would permit funds in Puerto Rico's Development Bank to be used for investment loans elsewhere in the Caribbean. And finally, he said the United States will help underwrite a $5.5 million program to modernize the judicial systems of Caribbean islands.