Havana has said it is not interested in rejoining the group.
Clinton has repeatedly said the US will not support Cuba's re-entry until it embraces the democratic principles outlined in the group's charter, halts human rights violations and releases political prisoners.
"It's not about reliving the past. It's about the future and being true to the founding principles of this organisation," Clinton told Caribbean foreign ministers before the summit began.
|Clinton said she is confident a compromise on Cuba could be reached [AFP]
"We do look forward to the day when Cuba can rejoin the OAS, but we believe that membership in the OAS must come with responsibilities."
Clinton was due to address the OAS later on Tuesday.
"I'm confident we can come up with a common way forward."
The US stance on Cuba has left it increasingly isolated in the region as Latin American countries have restored diplomatic relations with Cuba and pushed for an end to a crippling US economic embargo.
However, since taking office in January, the Obama administration has called past US policy a failure and moved to strengthen ties with the Caribbean island.
In April, Washington lifted curbs on travel to Cuba, as well as money transfers, by Cuban-Americans with relatives in Cuba.
It has also announced in the last few days that Cuba had agreed to resume talks on immigration to the US and begin discussions on direct mail links.