The White House says the vice president made the unannounced visit Wednesday and was received by the king's family, including Abdullah's son Prince Miteb bin Abdullah.
Biden delivered a personal letter from President Barack Obama for the 86-year-old Abdullah that wished him a quick recovery, the White House says.
Abdullah arrived in New York on Nov. 22 for medical treatment for what the palace said was a slipped disk and a blood clot pressing on nerves in his back.
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