Cuba was excluded from the summit, which brought together all 34 other countries from the Americas.
But Cuban President Raul Castro on Thursday said: "We are open, whenever they (US officials) want, to discussing everything: human rights, freedom of the press, political prisoners, everything, everything, everything they want to discuss."
That specificity was unprecedented, although Castro reiterated that talks could only take place if Cuba was treated as the United States' equal.
Unprecedented, too, was US Secretary of State Hillary Clinton's assessment just before the summit on Friday that US policy towards Cuba had "failed."
That admission came as Latin American nations increasingly criticized the 47-year-old US embargo on Cuba that has stunted its economy and contributed to the widespread poverty on the communist island.
The speed with which the United States and Cuba appeared to be ready to thaw an enmity held over since the Cold War was startling.
It seemed to have much to do with Obama's diplomatic touch at odds with the hardline stance of his predecessor, George W. Bush, who had tightened restrictions on Cuba.
The impetus for the conciliatory overtures came from Obama's decision early this week to lift curbs on Cuban-Americans traveling and sending remittances to Cuba.
Although former Cuban leader Fidel Castro dismissed the gesture as inadequate, it stirred other Latin American countries, most of which had already called in a summit in December for an end to the embargo.
Argentine President Cristina Kirchner, the first head of state to address the Trinidad summit, called the US embargo "anachronistic," a throwback to the "bipolar world" when the United States and the Soviet Union competed. It should be lifted, she said.
The left-wing presidents of Venezuela, Bolivia, Nicaragua and Honduras issued a joint statement Friday before heading to the summit saying they would not back the prepared final declaration because it was "insufficient and unacceptable" in several regards.
The summit "unjustifiably excludes Cuba, without mentioning the general consensus that exists the region condemning the blockade and attempted isolation" of the island, Venezuelan President Hugo Chavez said, reading from the statement.
Obama, who ruled out meeting with Chavez on the sidelines of the Americas summit, said in his prepared speech that his goal was seeing democracy in Cuba.
"We all have a responsibility to see that the people of the Americas have the ability to pursue their own dreams in democratic societies," he said.
"Toward that end, the United States seeks a new beginning with Cuba," he said.
The US president acknowledged that "overcoming decades of mistrust" would be difficult, but "critical steps" such as his scrapping of the curb on travel for Cuban-Americans were possible.
More generally, he said, he wanted to open a new era of equal partnership with all the nations of the Americas, some of which retain bad memories of overbearing US meddling in the past.
"I pledge to you that we seek an equal partnership," Obama said.
"I am here to launch a new chapter of engagement that will be sustained throughout my administration."