Most Latin American countries want the Caribbean island to return to the group, from which is was expelled in 1962, without preconditions.
But US Secretary of State Hillary Clinton said Cuba should only return if it passed democratic reforms.
Mrs Clinton said no consensus had been reached on the first day of the summit.
Cuba, which was expelled from OAS after the 1962 communist revolution, has said it would not accept membership if offered.
Cuban Foreign Ministry official Carlos Fernandez said reversing the expulsion would be "a good sign for the Organisation of American States" but that his country had no intention of rejoining the group.
'Common way forward'
Honduran President Manuel Zelaya told leaders at the annual two-day summit that the decision to expel Cuba - following the revolution which turned the country into a one-party communist state - was "a day that will live in infamy".
He said it was "time to correct that mistake", or the 34 members of the group would be "colluding with that mindset of yesterday".
His view was echoed by Nicaraguan President Daniel Ortega, who said the expulsion of Cuba had been "imposed by tyrants".
"As long as that sanction is not lifted, we continue to be accomplices of the sanction, therefore we lose dignity, we lose sovereignty," said Mr Ortega, accusing the US of using the organisation as "an instrument of domination".
But in a meeting with Caribbean leaders, Mrs Clinton said that while the US looked forward to Cuba rejoining the group, "membership in the OAS must come with responsibilities".
"It's not about reliving the past. It's about the future and being true to the founding principles of this organisation," she said.
"I'm confident we can come up with a common way forward."
Mrs Clinton has now left the summit but said negotiations would continue in her absence, the Associated Press reported.
'Humiliating'
President Barack Obama has introduced some changes to US ties with Cuba, including ending restrictions on Cuban-Americans visiting and sending money to relatives.
Washington and Havana have also agreed to resume regular talks on migration issues.
But the US has repeatedly said that Cuba must introduce democratic reform and release political prisoners before it can be re-admitted to OAS and before the decades-long embargo on it can be lifted.
The BBC's Michael Voss in Havana says Cuba's former leader, Fidel Castro, has called the US preconditions "humiliating and arrogant", while the current leadership has also shown no signs that it intends to meet Washington's demands.
There is now a real possibility that the US, the only American country which does not have diplomatic relations with Cuba, will be outvoted at the OAS, says our correspondent.
