Images distributed by the body showed dozens of people, mostly men, massing at the gates to the town's migration headquarters.
Around 250 people, mostly Cubans who entered Colombia illegally, are stranded near Panama, which has shut its border crossings in an attempt to stem the flow of undocumented immigrants, authorities said.
Panama last week became the third Central American country to halt access to an unrelenting exodus of Cubans trying to reach the United States by land.
The body that monitors human rights in Colombia, where the migrants are stranded, said that "to date there are about 250 undocumented immigrants" in the town of Turbo, located in the jungle on the Gulf of Uraba.
The human rights body said it had received "complaints from migrants about unscrupulous people who were eager to charge large sums of money in exchange for making arrangements in Bogota for passage into Panama."
Images distributed by the body showed dozens of people, mostly men, massing at the gates to the town's migration headquarters.
The immigration authority told AFP it was continuing to analyse the situation before taking any action.
Thousands of Cubans are leaving their island, typically by flying to Ecuador or other countries in South America to make a long overland trek through Central America and Mexico to try to get to the United States.
Under a US law dating back to the Cold War, Cubans who reach US soil -- whether by plane, foot or boat -- are allowed to stay and to work. Those spotted and picked up at sea, in contrast, are returned to the Communist-ruled Caribbean nation.