US President Barack Obama has said it is now up to Cuba to make the next move if relations are to be further improved.
He said the US expected Cuba to "send signals that they're interested in liberalising". He also cautioned that relations would not mend "overnight".
Mrs Clinton made her comments about Cuba in the Dominican Republic, ahead of the Summit of the Americas that begins in Trinidad and Tobago later on Friday.
"We are continuing to look for productive ways forward because we view the present policy as having failed," she said at a press conference.
"We welcome his comments and the overture they represent, and we are taking a very serious look at how to respond," Mrs Clinton said.
Cuba is excluded from the summit, which includes 34 members of the Organisation of American States (OAS), though Latin American leaders have been calling for the communist country to be readmitted.
OAS Secretary-General Jose Miguel Insulza said on Friday he would ask the organisation's members to readmit Cuba, 47 years after it was suspended.
Mr Insulza said he would put the proposal to a meeting of the OAS general assembly in Honduras at the end of May.
Speaking to Latin American leaders in Venezuela on Thursday, President Castro said he had sent word to the US government "in private and in public" that he is open to negotiations as long as they are "on equal terms".
Venezuelan President Hugo Chavez said he would veto the final declaration from the OAS summit because of Cuba's exclusion.
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