Rajaa al-Naser, another NCB member, said reporters that Brahimi would have more meetings with Syrian officials.
The international envoy had he met with Assad on Monday. Assad said he is keen to make any efforts successful so long as they come in the framework of preserving Syria's sovereignty and independence and serve the Syrian people's interests.
On Tuesday, China welcomed Brahimi's visit to Syria and wished him a fruitful trip.
"China is gravely concerned about the Syrian situation" and urges all Syrian parties to take into account the people's fundamental and long-term interests and "take actions to support Brahimi's mediation efforts," Chinese Foreign Ministry spokeswoman Hua Chunying told reporters.
She called on both the Syrian government and the opposition to follow the consensus reached in the Action Group Geneva Communique on the peaceful settlement of the Syrian issue, open inclusive political dialogues, negotiate a roadmap for political transition and establish a transitional body of broad representation in order to put an early end to the Syrian crisis.
Gulf Cooperation Council (GCC) leaders on Tuesday stressed the importance to move toward a Gulf Union and develop a "common defense system" to deal with any threats in the region, as the two-day 33rd GCC Summit was closing in Manama
In a final communique, the leaders also called on the international community to act against the massacres in Syria.
Ministry urges school safety after fatal van crash