"The vice president was received by King Abdullah's family," including one of his sons, the White House said in a statement. "During his visit with King Abdullah's family, the vice president delivered a personal letter from President Obama for the king, wishing him a speedy recovery."

The king flew to New York for medical treatment on Nov. 22 following a slipped disc and a blood clot pressing on the nerves in his back.

The king had surgery on his back at the New York Presbyterian Hospital to extract the clot on Nov. 24. Health Minister Dr. Abdullah Al-Rabeeah said afterward that his health was "very reassuring."

King Abdullah underwent a second successful operation on Dec. 2 to stabilize several vertebrae on the spinal cord to complement the previous surgery, the royal court said in a statement carried by the Saudi Press Agency.