Cuban officials and ordinary citizens alike have hailed the island's removal from the US list of state sponsors of terrorism.
They said the move by President Barack Obama heals a decades-old insult to national pride and clears the way to swiftly restore diplomatic relations.
"The Cuban government recognises the president of the United States' just decision to take Cuba off a list in which it should never have been included," Josefina Vidal, Cuba's senior diplomat for US affairs, said.
Cuban and US foreign-policy experts said the two governments appeared to have taken a major leap toward the reopening of embassies in Havana and Washington after four months of complex and occasionally frustrating negotiations.
In a message to Congress, Mr Obama said Cuba's government "has not provided any support for international terrorism" over the last six months and has given "assurances that it will not support acts of international terrorism in the future".
Cuba will officially be removed from the terrorism list 45 days after the president's message was sent to Congress.
Politicians could vote to block the move during that window, though Mr Obama would be all but certain to veto such a measure.
What remains to be seen in coming weeks is whether Cuba will allow US diplomats to move around Cuba and maintain contacts with citizens including dissidents, the second point of contention in the negotiations on restoring full diplomatic relations.
Cuba is highly sensitive to any indication the US is supporting domestic dissent and that issue may prove considerably tougher than amending the terrorism list.
The Obama administration made little pretence in recent years that it believed Cuba was supporting terrorism.
Cuba was put on the list in 1982 because of what the US said were its efforts "to promote armed revolution by organisations that used terrorism".
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