The leaders express their sincere condolences and sympathy to King Salman.
The measures were put in place in light of emerging indicators of "an increase in the epidemic curve" in some regions.
Kuwait has also advised citizens against non-essential travel amid new Covid strains.
Ministry urged citizens to ensure health insurance if travelling.
Ministry of Interior announced the move based on Health ministry's advice.
The borders were closed on January 19 because of concerns about a new coronavirus variant, a measure that was extended last week.
Earlier, Saudi Arabia had thwarted a missile attack.