Mr Castro, who had not spoken at the event for the past two years, grabbed the microphone to address the crowd in the eastern province of Guantanamo.
He said he would hold talks with the US, as long as it was "a conversation between equals".
The two countries have not had diplomatic relations for five decades.
President Castro said the offer had already been made through diplomatic channels and that no topic was off limits.
"Any day they want, the table is set," Mr Castro said.
He said he was prepared to discuss "the problems of democracy, human rights etc. But on equal terms because we are no-one's colony".
On Wednesday, the White House called the arrest of a group of dissidents attending the funeral of activist Oswaldo Paya "a stark demonstration of the climate of repression in Cuba".
President Castro said Cuba would remain independent and free, and nothing like the uprisings in Libya or Syria, backed by foreign forces, would happen in the country.
If the US wanted confrontation, he quipped, then it should be in baseball or some other sport.
"Preferably baseball when sometimes they win, sometimes we do," he said.