He also warned that Cuba faced a "long and difficult struggle" before the US removed its economic embargo.
On Wednesday, President Barack Obama announced a "new chapter" in US ties with communist-run Cuba.
He said the changes were the "most significant" in US policy towards Cuba in 50 years.
US-Cuba relations have remained frozen since the early 1960s, when the US broke off diplomatic relations and imposed a trade embargo after Cuba's revolution.
'Outdated' approach
Speaking in the National Assembly in Havana, President Castro said this week's announcement by Mr Obama removed an "obstacle" in bilateral relations.
Mr Castro said he was open to discussing a wide range of issues with Washington, but stressed that Cuba would not give up its socialist principles.
"In the same way that we have never demanded that the United States change its political system, we will demand respect for ours."
Mr Castro added that Cuba had to go through a "long and difficult struggle" before the decades-old US economic embargo would be lifted.
Announcing the normalisation of diplomatic and economic ties, President Obama said Washington's approach towards Cuba was "outdated".
As part of the deal, US contractor Alan Gross and an unnamed intelligence officer loyal to the US were released from Cuban prison in return for three Cubans held in the US.
Mr Obama also said he wanted to reopen a US embassy in Havana in the coming months.
Key dates
1959: Fidel Castro and his guerrilla army defeat the US-backed Cuban regime of Fulgencio Batista
1960-1961: Cuba nationalises US businesses without compensation; US breaks off diplomatic relations and imposes a trade embargo in response
1961: Failed Bay of Pigs invasion by CIA-backed Cuban exiles
1962: Soviet Union deploys ballistic missiles to Cuba, prompting Cuban Missile Crisis
2001: Five Cubans, dubbed the Cuban Five, are jailed in Miami for spying
2008: Raul Castro becomes Cuban president
2009: US citizen Alan Gross detained in Cuba accused of spying
Dec 2013: US President Barack Obama and Raul Castro shake hands at Nelson Mandela's funeral - the first such public gesture since 1959
17 December 2014: Alan Gross is released by Cuba
