The king, born in 1924, has spent time in Morocco recovering after operations in recent years.
But SPA published pictures showing princes and officials greeting the king at Jeddah airport before his departure for Morocco, where the royal family has properties in Casablanca and the southwestern port of Agadir.
The report challenged rumours in the media that the ageing monarch's health had deteriorated seriously.
King Abdullah is still having difficulty walking after two operations in October 2011 and November 2012 to correct a "ligamentary slackening" in the upper back.
Doctors discharged him from hospital in December last year.
The king's age and his hospitalisations regularly give rise to rumours about the future leadership of the kingdom, which is the world top oil exporter and a key player in the Middle East.
His half-brother Prince Salman, born in 1935, was named crown prince in June last year after the death of Prince Nayef bin Abdul Aziz.