"I can assure that the health of King Abdullah is excellent and gives no cause for any concern," a senior embassy official told AFP.
An informed source told AFP: "These are baseless rumours. The king is alive and well, and he has held several audiences since his telephone call with Obama."
The website www.islamtimes.org said in a Thursday article that King Abdullah had died of a heart attack the previous day after a heated telephone debate with US President Barack Obama on the situation in Egypt.
The Times of London reported on Thursday that in a "testy, personal" telephone call with Obama on January 29, the king had threatened to bankroll the Egyptian regime if the US withdrew its aid.
He also warned Washington not to humiliate veteran Egyptian President Hosni Mubarak saying he should be allowed to stay on to oversee the transition, the Times added, citing a senior source in Riyadh confirmed by two other sources.
King Abdullah arrived in Morocco on January 22. He had flown to New York on November 22 and was operated on two days later for a debilitating herniated disc complicated by a haematoma that put pressure on his spine.
That surgery was declared a success, as was a second operation to repair several vertebrae.
The monarch's advanced age combined with his back hernia raised concerns about the future of Saudi Arabia, which has been ruled by the Al-Saud family since 1932.
The crown prince, Abdullah's half-brother Prince Sultan bin Abdul Aziz who has been defence minister since 1962, is also in his mid-80s and has been slowed by what is believed to be cancer.
Little seen for the past two years, Sultan flew home from Morocco on November 21 to assume control of the royal government in Abdullah's absence.
The North African kingdom is a favourite holiday destination for Saudi royals who own private palaces here.
Prince Nayef, 77, is the king's half-brother and is third in line to the Saudi throne. He was appointed second deputy prime minister in March 2009.