The exiles said they supported the dissidents on the island in their refusal to vote.
The six House members said they opposed the U.S. embargo on Cuba and wanted travel restrictions to the island for U.S. citizens lifted.
They asked the members of the opposition present at the meeting for a vote at that moment on whether they supported the embargo.
The Cuban activists refused, and said that in no way did they represent all of the Cuban opposition, and therefore, a vote on their part would be representative.
The dissidents in Cuba interpreted the action as an attempt to use them in support of anti-embargo forces in the United States.
Among those at the meeting was Osvaldo Paya Sardinas of the Christian Liberation Movement, who said the action was an attempt to use the opponents of the Fidel Castro regime to support the end of the embargo.
"Don't ask us anymore, whether we want an embargo of investment, tourism or other exchanges," Paya was quoted as saying. "Ask us how Cubans, who cannot travel, own their own businesses, or express themselves freely, are trying to participate in the affairs of their own country."
"Paya made it very clear to members of Congress that the priority is not investment but how are we going to help people in Cuba, how are they going to participate and that to Paya is priority No. 1," said Jose Basulto, founder of the Cuban-American group Brothers to the Rescue.
"This was an arrogant act (by the delegation) to ask them for a vote in favor of lifting the embargo," Basulto said. "They (the Cubans) saw it as a manipulation."
He said they left their feelings for or against the embargo completely off the table.
The Miami group of exile organizations also said it opposes an economic relationship between the two countries without political or social reforms, as Raul Castro, Fidel Castro's brother, suggested Saturday.
"Today we call upon our brothers in the exile community to voice together with us, their support for Paya's statement in behalf of the legitimate voices of the island," the group said in a statement.
The congressional delegation consisted of Reps. William Clay, D-Mo.; Jo Ann Emerson, R-Mo.; Hilda Solis, D-Calif.; William Delahunt, D-Mass.; and Stephen Lynch and Victor Snyder, D-Ark.