HAVANA, March 21 (Reuters) - U.S. President Barack Obama pushed Cuba to improve its record on human rights and sparred with President Raul Castro during a historic visit to the Communist-ruled island on Monday, while Castro hit back by decrying U.S. "double standards."

Human rights remained an impediment to strengthening ties with Cuba despite the rapprochement reached by the two leaders in December 2014, Obama said, adding a "full flowering" of the relationship could happen only with progress on the issue.

"In the absence of that, I think it will continue to be a very powerful irritant," Obama said at a sometimes tense joint news conference that was broadcast live on Cuban state television. Castro appeared at times uncomfortable and showed flashes of anger as he made the rare step of taking questions from journalists.

Obama, the first sitting U.S. president to visit Cuba in nearly 90 years, is under pressure from critics at home to push Castro's government to allow political dissent and to further open its Soviet-style economy. Some opponents of the visit say he has already given away too much as he improves ties, with too little from Cuba in return.