Obama shook Castro's hand Tuesday as he walked down the line greeting other leaders, including Indian President Pranab Mukherjee, gathered there to pay their respects to South Africa's first black president who died Thursday.
Later a White House official told reporters that the moment was not "a pre-planned encounter", and the two exchanged nothing more substantive than a greeting.
"Above all else, today is about honouring Nelson Mandela, and that was the president's singular focus at the memorial service. We appreciate that people from all over the world are participating in this ceremony," Obama aide Ben Rhodes said.
The US president also greeted Brazilian President Dilma Rousseff, who has filed a formal protest with the US and rebuked the National Security Agency for its eavesdropping on world leaders.
Obama is not the first US President to shake hands with a Cuban leader. In September 2000, then-President Bill Clinton and Fidel Castro shook hands at the UN in what Secretary of State Madeleine Albright called a "chance encounter".
"Though undoubtedly a polite gesture meant to honour Mandela's legacy, the handshake also comes not long after Obama indicated a desire to update US policies toward Cuba," noted influential Washington political news portal Politico.
"The question is whether Mr. Obama was trying to signal a desire to change hearts by shaking Mr. Castro's hand," wondered the New York Times.
"If so, the Cuban president would become the latest adversary that Mr. Obama has sought to turn into a friend - or at least a less dangerous opponent. Mr. Obama's efforts to negotiate a nuclear deal with Hassan Rouhani, the Iranian president, is another example," it noted.
But "a handshake like the one Mr. Obama offered Mr. Castro has the potential to become a political problem for the president, much the way that Mr.Obama's handshake in 2009 with Hugo Chavez, then the socialist president of Venezuela, was criticized by Republicans," the Times said.
Sure enough Republican leaders were quick to criticise Obama with his 2008 Republican presidential opponent Senator John McCain comparing the gesture to (then British prime minister) Neville Chamberlain's handshake with Adolf Hitler at the start of World War II.
"It gives Raul some propaganda to continue to prop up his dictatorial, brutal regime, that's all," McCain said sarcastically. However, Cuban American Senator Marco Rubio suggested Obama should have taken the opportunity to press Castro on human-rights issues.
Republican House member Ileana Ros-Lehtinen, who was born in Havana before her family moved to Miami, said it was "nauseating and disheartening" to see the handshake.
Fellow Republican representative Mario Diaz-Balart, another son of Cuban immigrants, said "the president's friendly demeanour with Raul Castro is reflective of his policies to the Castro regime and every other terrorist dictatorship".
But Paul Begala, a Democratic strategist, who was a political consultant for Bill Clinton's presidential campaign in 1992 and was counsellor to Clinton in the White House, asserted "Obama was right to shake hands with Raul Castro".
"I believe Obama shook Raul Castro's hand for the same reason Reagan shook Gorbachev's or Mandela shook that of F.W. de Klerk, the last president of an apartheid South Africa: because he knows he's on the right side of history," he wrote in a CNN commentary.
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