In his first public comments since Castro temporarily transferred power to his brother, Raul, due to illness Bush said on Thursday: "We have repeatedly said that the Cuban people deserve to live in freedom.
"We will support you in your effort to build a transitional government in Cuba committed to democracy, and we will take note of those, in the current Cuban regime, who obstruct your desire for a free Cuba."
His comments reinforced the stated US line that it does not support the handover of power to Raul, who took over on Monday due to his brother’s need for intestinal surgery.
However, it remains unclear whether Raul is fully in charge. Fears of a power vacuum were raised when he failed to appear publicly again on Thursday.
Instead the only news from him was in the form of a reprint of a speech he made on July 1 discussing the legitimacy of the country's leadership, published in the Communist newspaper Granma.
Bush said the United States was "actively monitoring the situation in Cuba".
Earlier Sean McCormack, a state department spokesman, said the transfer of power to Raul "denies the Cuban people of their right to freely elect their government".
Proof that Raul is in the seat of
power has yet to be provided
He also pledged humanitarian aid to Cuba to support a "genuine transition".
Changes in the US policy towards Cuba, particularly in the area of immigration, are rumoured to be afoot after politicians from Florida, where the large exiled Cuban-American population celebrated Fidel’s illness, met with Washington officials on Wednesday.
Some experts on the regime are not surprised Raul is taking his time but nevertheless speculation has increased as to what the political future of the island may hold after Fidel Castro.
Many people out on the streets said they were not familiar with Raul, who was seen as a hardliner during the early days of the communist regime but is now said to admire China’s economic policy and to have led reforms such as opening Cuba up to tourism.
Fidel Castro, who turns 80 on August 13, has been heard from only in a statement attributed to him late on Tuesday and was last seen in public on July 26.
His sister Juanita, a drugstore owner in Miami, has told US media that she had been told her brother Fidel was out of intensive care.
"We have repeatedly said that the Cuban people deserve to live in freedom"
But Internet bloggers have debated whether Fidel might already be dead.
On Wednesday, the conservative Cuban American national foundation urged Cuba's armed forces not to follow Raul's path.
Jorge Mas Santos, the foundation's president, said: "There is now an opportunity for brave men and women who want to take Cuba in another direction to take advantage of that opportunity."