More than 115,000 people have been killed in the 31-month armed uprising against the Assad regime triggered by his forces' bloody crackdown on Arab Spring-inspired democracy protests.
Brahimi has been travelling throughout the Middle East to drum up support for Geneva peace talks, and the Syrian leg of the tour is the most sensitive as he needs to persuade a wary regime and an increasingly divided opposition to attend.
A diplomatic source told AFP he was to hold talks with Assad in the morning, and journalists said he was later seen leaving his Damascus hotel with Syrian Deputy Foreign Minister Faisal Meqdad in a convoy of UN cars.
"Syria will attend Geneva II based on the exclusive right of the Syrian people to choose their political future, to choose their leaders and to reject all forms of external intervention," Foreign Minister Walid Muallem told Brahimi.
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He also said all statements about the country's future, especially "the one from London", were "infringements on the rights of the Syrian people" and "preconditions to the dialogue before it has even started".
That was a reference to an October 22 meeting at which Assad's opponents and countries that back them -- including the United States -- declared he had no future role to play in Syria.
The Algerian envoy added there was agreement on "the importance of ending the violence, terrorism and respecting Syrian sovereignty," according to SANA.
The main opposition National Coalition has said it will refuse to attend any talks unless Assad's resignation is on the table, and some rebel groups have warned anyone who goes will be considered a traitor.
In a defiant interview broadcast earlier this month, Assad himself cast doubt on the possibility of talks, saying he will not negotiate with any group tied to the rebels or to foreign states.