The kingdom has witnessed bouts of unrest in recent months, including scattered protests against a curfew and economic hardship triggered by the coronavirus pandemic.
The three countries agreed on the resolution during a video-conference with Egyptian counterpart Abdel Fattah al-Sisi and Jordan's King Abdullah II, said the statement.
Bassem Awadallah, seen as an influential figure familiar with the inner workings of the Saudi leadership, was ensnared in a rift within Jordan's royal family that played out in full public glare.