Cuban President Raul Castro has urged the US to end its trade embargo after the two countries opened formal talks on restoring diplomatic relations.
He said the five-decade embargo “caused enormous human and economic damage”.
But only the US Congress has the power to lift the embargo, and correspondents say many Republicans are still deeply opposed to this.
On Wednesday, US President Barack Obama and Mr Castro agreed a number of measures to improve ties.
They included the release by Cuba of US contractor Alan Gross and three Cubans held in the US.
Relations between the US and Cuba have been frozen since the early 1960s when the US broke off diplomatic relations and imposed a trade embargo after Cuba’s revolution led to communism.
But in unprecedented moves on Wednesday, Mr Obama said the “rigid and outdated policy” of isolating Cuba had clearly failed.
He said economic reforms were still needed in Cuba and human rights there needed to be upheld. But he said it was time for a new approach.
Mr Obama added that the US was looking to open an embassy in Havana in the coming months.
The trade embargo on Cuba, however, cannot be lifted without approval by Congress and correspondents say Mr Obama may struggle to pass the legislation.
Bells ring out
Wednesday’s announcements follow more than a year of secret talks in Canada and at the Vatican, directly involving Pope Francis.
In his televised address on Wednesday, President Castro said Cuba was willing to discuss differences that remain with the US on national sovereignty, democracy and internal policies.
“We should learn the art of living together in a civilised manner in spite of our differences,” he said.
As he spoke, church bells rang out and schools paused their lessons to mark the news.
Officials said that Mr Obama and Mr Castro spoke by telephone on Tuesday for nearly an hour – the first presidential-level talks between the two nations since Cuba’s 1959 revolution.
Mr Gross, 65, who is in poor health, was detained by the Cuban authorities five years ago for importing banned satellite technology.
His arrest and imprisonment had undermined previous attempts to thaw diplomatic relations between the two countries.
Cuba and the US said he had been freed on humanitarian grounds.
Cuba also freed an unnamed American intelligence officer who had been in jail in Cuba for nearly 20 years.
In exchange, Washington released three high profile Cuban prisoners who were serving lengthy sentences for espionage.
They were part of the so-called “Cuban Five” who US prosecutors said had sought to infiltrate US military bases and spied on Cuban exiles in Florida.
Two of them had recently been allowed to return to Cuba after finishing their sentences.