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.

In announcing the new travel policy, the Obama administration said people-to-people exchanges would support civil society as well as the free flow of information.

This year, it also loosened regulations for educational and religious trips to Cuba allowing universities, schools and religious organizations to make trips without seeking licenses from Washington. A Florida law, however, bars public schools and universities from funding Cuba trips but other students may go as long as they receive credit.

The new rules are not playing well with South Florida’s Cuban-American Congressional delegation. Rep. Mario Diaz-Balart, and Rep. David Rivera, both Republicans, have introduced amendments that reset the Cuban travel policy to the more restrictive regulations of the Bush administration, not only eliminating people-to-people exchanges but also barring Cuban-Americans from visiting more than once every three years for family reunifications. Remittances also would be limited to $1,200 and the definition of who qualifies as family tightened up.

President Obama has threatened a veto.

Earlier this month, Republican Rep. Ileana Ros-Lehtinen wrote a letter to Treasury’s Office of Foreign Assets Control after she saw a travel agency quoted in a Louisiana newspaper saying the “first wave of pure tourists from America will hit the friendly skies Aug. 11.’’ She called that an “egregious misrepresentation’’ of the travel guidelines and wanted to know what OFAC was doing to prevent or correct such activity by travel agents.

OFAC issued an advisory Monday saying it was aware of media misstatements giving the impression that the “U.S. now allows for virtually unrestricted travel to Cuba.’’

It reminded travelers that there are regulations governing such travel, including spending limits and a prohibition on buying any souvenirs except for informational materials.

Travel organizations that have received licenses say Treasury has been strict, sometimes asking for additional details and definitions, and insisting that there be meaningful interactions between Cubans and travelers.

“These trips are highly structured. We spend no time at the beaches and will be concentrating on historic sites,’’ said Burt Altman, a retired professor who with his wife Norma will be directing an April 2012 tour for Learning in Retirement, a program geared for retired or semi-retired people that is affiliated with the University of Wisconsin La Crosse.

One of the stipulations of the license, he said, was that “people would be kept busy at all times.” Most of the people-to-people trips will leave from Miami and don’t include airfare.

Insight Cuba, which will take 16 people per group, sent out its application for a license the day guidelines were issued in the Federal Register in January. “We knew something would change, so we kept up our relationships in Cuba,’’ said Tom Popper, director of Insight Cuba. “It was like lifting the hood of a car that had been in the garage and figuring out what needed to be done to get the trips going again.’’

Among the attractions on Insight Cuba’s eight-day music and art experience, which starts at $2,495, are a meeting with Afro-Cuban artists, a visit to Egrem, Cuba’s largest recording label, and salsa lessons.

In the next year, Popper said, Insight Cuba is offering 130 departure dates and hopes to take 5,000 to 7,000 Americans to Cuba.

If no restrictions are placed on the new people-to-people policy, thousands more Americans are expected to travel to Cuba this year and next.

Last year 63,000 U.S. citizens visited, according to the Cuban government. But that number pales compared to the number of Cuban-American travelers, who are counted separately from other U.S. visitors to the island.

Air charter providers to Cuba estimate around 320,000 Cuban-Americans visited in 2010 — although some of those travelers made multiple trips.

By next year, the face of travel to Cuba could look quite different, said Bob Guild, vice president of Marazul Charters.

It’s too early to estimate the numbers of travelers on people-to-people exchanges, Guild said, but he expects academic travel to become a “large category.’’ Already, he said, Marazul has requests from two dozen schools for trips in January and February.

And he expects Cuban-American travel to continue to grow with as many as 375,000 to 400,000 people making trips in 2011.