The Reagan administration moved yesterday to solve some of the problems remaining from last year's food of Haitian and Cuban refugees into south Florida, reaching an agreement to move 800 Haitians to Puerto Rico and beginning a program to release some of the 1,800 Cubans in federal prison in Atlanta.

In a related development, Sen. Walter (Dee) Huddleston (D-Ky.) charged with the administration is violating the 1980 Rufugee Act by continuing to process Indochinese "boat people" as refugees after the Immigration and Naturalization Service ruled that many were fleeing for economic, rather than political, reasons.

The law says that, to be classified as refugees, people have to have a "well-founded fear of persecution," political, religious, or otherwise, rather than be fleeing for economic reasons. Under previous policy, those fleeing communist regimes automatically were classified as refugees.

In introducing a Senate resolution yesterday, Huddleston called for an investigation and suggested that the program to accept up to 168,000 Indochinese a year be phased out if the findings warranted it.

Federal authorities feel that the Haitians, especially, have entered the United States for economic reasons and should be deported after due process hearings. Some who support the Haitians' bid to remain in the country view the different treatment of the Indochinese as a double standard.

Shep Lowman, director of the State Department's Asian refugee resettlement program, responded that his department's judgement is that the Indochinese would be persecuted if forced to return to their homelands, while the Haitians would not.

Lowman also noted that only 86,000 of the authorized 126,000 refugees from Vietnam, Laos, or Cambodia have entered the United States through June.

Associate Attorney General Rudolph W. Giuliani, who negotiated the agreement to use Fort Allen in Puerto Rico with Gov. Carlos Romero, praised commonwealth officials for being willing to "share the burden." He said the government still plans to detain some arriving Haitians at the Krome North facility near Miami, but the agreement will avoid overcrowding at that camp.

Guiliani said that the new look at the 1,800 Cubans held in Atlanta will set standard procedures.

When the flood of Cubans entered the United Stats early last year, those who admitted having criminal records were kept in prisons rather than camps. Most have been there ever since, because Cuban Premier Fidel Castro has refused to consider taking them back. Now, those found to be nonviolent and unlikely to commit crimes will be eligible for release to a sponsor.