Columbia, S.C. — The message to President Reagan from the Caribbean is economic. Give us more aid, more trade, and more investment, say leaders and representatives of 15 Caribbean nations and territories gathered here for a two-day conference. Some of the leaders complain President Reagan's Caribbean Basin initiative, aimed at long-term economic development of the region, has lost momentum.
The preoccupation with Cuba and its influence, which dominated discussions among some of these same Caribbean leaders a year ago, no longer tops the list of subjects for discussion.
''Our problems ... are not military but social and economic,'' said Prime Minister John Compton of St. Lucia at the opening session of what is being called a Caribbean summit meeting.
President Reagan will meet with the Caribbean leaders today.
Prime Minister Compton praised the US invasion of Grenada last October - he called it a ''rescue mission'' - but he said the problems now facing the Caribbean are ''not amenable to military solutions.''
Nicholas Brathwaite, head of the interim government of Grenada, described the economic situation on his small island as ''grim.''
Speaking for the island of Barbados, Prime Minister Louis R. Tull said the economic problems confronting the entire region were so severe that they ''threaten our very security.''
The democratic nations of the Caribbean are relatively small, ranging from islands of fewer than 100,000 people, such as Grenada, up to the 6 million residents of the Dominican Republic, the region's largest democracy. But the Reagan administration considers these islands to be of great strategic importance, given their proximity to the US and the sea lanes that pass close to them.
In recent years, most of these nations have had to face what President Reagan himself once described as an ''economic siege.'' The rise in world oil prices and a drop in the prices of the island's main exports, combined with the world economic recession, have had a disastrous impact.
But as James B. Holderman, chairman of the opening meeting at the conference and president of the University of South Carolina, explained it, the attention of US policymakers and the American public has tended to be diverted away from the Caribbean by other seemingly more-pressing problems, including the current unrest in Central America.
Efforts now under way to broaden regional alignments in the Caribbean could give the island nations more influence in Washington, however. Nations of the east Caribbean grouping known as CARICOM recently decided to invite the island nations of Haiti and the Dominican Republic to attend their meeting as observers. Until recently, CARICOM has amounted to a club of former British colonies.
Salvador Jorge Blanco, president of the Domincan Republic, is attending this week's conference of Caribbean leaders in South Carolina in what one conference participant called ''his foray into the Caribbean.''
President Jorge Blanco's participation in the conference marks a step toward breaking some of the linguistic, cultural, and historical barriers that have separated his Spanish-speaking nation from the English-speaking Caribbean. The Dominican Republic president was meeting some of his fellow-Caribbean leaders here for the first time.
Some participants at the South Carolina conference spoke of the opportunities that President Reagan's Caribbean Basin initiative (CBI) offers the region. But others were critical, questioning both the implementation of the program and the changes the US Congress had made in the CBI legislation. Those changes have tended to diminish trade benefits and investment incentives for the region.
At the opening session here, Carlos S. Quiros, secretary of state of the Commonwealth of Puerto Rico, was the most outspoken on the subject. He said there was increasing frustration in the region over what he described as the CBI's lack of momentum.
Mr. Quiros said the program suffered from ''an inability to translate noble hopes from theory into practice.''
The Puerto Rican secretary of state pointed to problems with the US Customs Service and disappointment that the US government had failed to establish a significant role for Puerto Rico in the CBI.