Cubans have marked Revolution Day without their ailing President, Fidel Castro, for the first time since 1959.
Raul used his speech to offer talks with the next US president
Acting leader Raul Castro led the day's events, filling in for his brother - who was last seen in public a year ago.
Raul said that the months without Fidel had been "difficult" but insisted that his brother was recovering well.
The holiday commemorates a rebel attack on the Moncada barracks in 1953 - credited with sparking the revolution that brought Fidel Castro to power.
The 80-year-old president temporarily handed over power to his brother on 31 July last year as he was due to undergo surgery.
An estimated 100,000 people packed into the main square in the city of Camaguey some 500km (300 miles) east of the capital, Havana.
The people nearest the stage all wore official red T-shirts and almost everyone was waving a Cuban flag.
But without Fidel Castro present, the mood appeared somewhat subdued, says the BBC's Michael Voss in Camaguey.
Raul Castro said his brother's illness had been a "hard blow".
"These have been difficult months but the outcome has been diametrically opposed to the hopes of our enemies, who dreamt that chaos would be unleashed and Cuban socialism would end in collapse," he said.
Raul again indicated that he might be open to a warming of relations with the US, which has maintained an embargo against Cuba for 45 years.
He reiterated an offer he made last December to speak to the US - but only after next year's presidential elections were over.
"If the United States authority were to finally desist from their arrogance and decide to converse in a civilised manner, it would be a welcome change," he said.
"Otherwise, we are ready to continue confronting their policy of hostility, even for another 50 years if needs be."
His remarks drew a quick reaction from the Bush administration.
"The only real dialogue he needs is with the Cuban people," said state department spokesman Sean McCormack.
"I think that if the Cuban people were able to express the opinion on the question of whether or not they would like to freely choose their leaders, the answer would probably be yes.
"Unfortunately, that is not the dialogue that is taking place in Cuba at the moment."
Series of articles
In 2006, Fidel Castro, as he had done for decades, delivered speeches to mark Revolution Day.
The transition of power from Fidel to Raul has been smooth
But five days later, it was announced that he was undergoing intestinal surgery and he temporarily handed over control of the government to Raul.
Since then there has been no indication of when - or if - Fidel Castro will resume his duties as president.
He has appeared only in photographs and videos, although he has voiced opinions on international affairs in a series of articles published by the official press.
"OK, he's not here, but Fidel is in our hearts and we continue to follow his ideas", a man at the Camaguey celebrations told the BBC.
Correspondents say 76-year-old Raul has none of his brother's charisma but has played a key role in recent Cuban history.
The transition of power has been smooth, and life in one of the world's last communist states remains largely unchanged.
No major initiatives are now expected until after a new assembly is chosen early next year, our correspondent says, and only then will Cuba's permanent leadership become clear.
Thursday's commemorations mark the attack on the Moncada barracks, when Raul was at Fidel's side along with about 100 poorly armed guerrillas.
Their uprising failed but the attack on the barracks became a rallying cry for the revolutionary movement that gained in strength and eventually topped Fulgencio Batista from power.