Washington has renewed a four-year-old offer to lift its trade embargo on Cuba if Havana embraces democratic reforms.
Castro's illness sparked new interest in the future of Cuba
Assistant Secretary of State Thomas Shannon said the offer was "still on the table" if the Cuban government would "begin a political opening".
Correspondents say the offer is nothing new, but the timing is significant.
It comes three weeks after Fidel Castro underwent surgery and temporarily ceded power for the first time to his younger brother Raul.
Mr Shannon told journalists that the administration would consult with Congress on lifting the 44-year-old trade blockade on Cuba in return for certain reforms.
These included freeing political prisoners, protecting human rights, permitting political parties, and creating a "pathway towards elections".
Hints at rapprochement
The BBC's Emilio San Pedro, in Miami, says the offer is identical to one made in 2002, and does not deviate from Washington's stance on Cuba since it declared the embargo 10 White House administrations ago.
But Mr Shannon's comments also come a few days after Raul Castro made comments hinting at a possible rapprochement to the official Cuban newspaper, Granma.
Mr Castro said that Cuba was willing to consider improved relations with Washington, if the Bush administration agreed not to interfere in Havana's internal affairs.
But he also said Havana remained "vigilant" and prepared to face a possible US invasion of the island.
On Wednesday, Mr Shannon also commented that although Raul Castro was the "heir apparent", he did not believe he would wield the same individual authority as his brother.
He said what would emerge would be "some kind of power-sharing arrangement" among institutions.
The US rejects suggestions it will attempt to foment a crisis in Cuba. It has however recently approved a new fund of tens of millions of dollars to support Cuban opposition movements.