Other Arab delegates also left Davos prematurely, ahead of the funeral of the Saudi king.
The early departure of Jordan's king forced the forum to change a session at which he was due to speak on Friday about Middle East security.
The forum, which gathers 2,500 political and business leaders in the Swiss Alps for four days of debate, said there would still be various sessions held on the Middle East on Friday, during which delegates would consider the news.
Abdullah had ruled Saudi Arabia as king since 2005, but had run the country as de facto regent for a decade before that after his predecessor King Fahd suffered a debilitating stroke.
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