Travel providers and other groups are scrambling to secure licenses and organize people-to-people exchanges in Cuba after a decision by the U.S. government to relax restrictions and allow a wider variety of Americans to visit the Caribbean island for the first time in 7 1/2 years.

So far, the Treasury Department has issued nearly 30 licenses to organizations that say they will provide “purposeful travel,’’ which will allow Americans to reach out to everyday Cubans in “support of their desire to freely determine their country’s future.’’

Although Cuba-Americans can now travel freely to the island if they receive a visa from Cuba and travel is allowed for other Americans who fall into a limited number of categories, the United States has barred people-to-people visits since the end of 2003 when former President George W. Bush reversed a policy begun during the Clinton administration.

Insight Cuba, a company that ran people-to-people exchanges prior to the rollback on such travel, looks like it will be first with the new people-to-people exchanges. It plans to send its first four groups to Cuba on August 11.

Groups ranging from the Harvard Alumni Association to luxury travel provider Abercrombie & Kent — it pitches its trip as “Cuba: The Forbidden Isle Revealed’’ — to Witness for Peace also are ready for Cuba travel.

There seems to be plenty of demand.

The Oct. 26-Nov. 1 Harvard trip, which promises to “unravel the richness of Cuban culture,’’ is waiting list only. A&K, which will be working with the Foundation for Caribbean Studies — the nonprofit that actually holds the license — began advertising last week for 13 trips it plans between September and next April. All have sold out.

“We knew there would be interest, but this is incredible,’’ said Jean Fawcett, an A&K spokeswoman. “We’re taking names for a wait list and are planning to add more trips in 2012.”

Witness for Peace says it will offer talk with “ordinary Cubans who will tell about their achievements, challenges and daily struggles.’’ Its 10-night-trip in December costs $1,550 — a relative bargain in the world of people-to-people exchanges.

A&K’s 10-night tours, in contrast, are priced from $4,325 double occupancy and cover a wide swathe of Cuba, visiting Cienfuegos, Trinidad, Havana and Matanzas.

A&K, which began as a safari outfitter in Kenya, promises its Cuba trips will meet the same high standards its travelers have come to expect.

Travelers will stay on a club-level-type floor at the Hotel Nacional, eat almost exclusively at paladares (home restaurants) whose menus have been planned with A&K staff, travel in new air-conditioned motor coaches with leather seats and go through VIP customs and immigration check-in, said Fawcett.

But along the way, she said, there will be plenty of opportunities to interact with Cubans. “We don’t want people to feel like tourists. We want this to be an authentic people-to-people exchange,’’ Fawcett said.

As part of the U.S. embargo against Cuba, for decades the United States has limited Americans from going to Cuba and spending money — although there have been exceptions for travelers such as Cuban-Americans, journalists, those on professional and academic research trips and people on humanitarian and religious missions.