Russia is seeking to revive last summer's peace plan for Syria in talks with a senior Syrian diplomat and an international envoy, according to Moscow's foreign ministry.
Syrian deputy foreign minister Faisal Mekdad met Russia's foreign minister Sergey Lavrov on Thursday and is expected to hold talks with other senior Russian diplomats, said Moscow spokesman Alexander Lukashevich.
Mr Lukashevich denies the existence of a new US-Russian peace plan. He says Russia is pushing for fulfilment of a plan brokered by Mr Brahimi's predecessor, Kofi Annan, which was approved at an international conference in Geneva in June.
He reaffirmed Moscow's objection to calls for Assad's removal.
Mr Brahimi described the situation as "worrying" after his talks with Assad.
After meeting the Syrian leader at the presidential palace in Damascus, he said he and Assad exchanged views on the conflict and discussed possible steps forward, which he did not disclose.
Syria's state news agency quoted Assad as saying his government supported "any effort in the interest of the Syrian people which preserves the homeland's sovereignty and independence".
Mr Brahimi called for the formation of a transitional government to run Syria until elections can be held. He told reporters in Damascus that political changes in Syria must not be "cosmetic" and should lead to genuine change while preserving state institutions.
Mr Brahimi did not specify the role of Assad in any new government. Rebels seeking to topple his regime refuse any role for Assad and top regime members. The Syrian government did not immediately comment on Mr Brahimi's suggestion.