Lebanese President Michel Suleiman met with Brahimi, who was expected to visit the Damascus, Syria, later in the day.
More than 30,000 people have been killed in Syria since the conflict began in March 2011, opposition activists say.
Dr. Jihad Makdessi, a spokesman for the Syrian Foreign Ministry, said Tuesday the government is "interested in exploring this [cease-fire] option" and in hearing about the position of other countries Brahimi visited in discussing a possible truce, DayPress reported.
However, Makdessi stressed the violence would end only if rebel forces were also involved in the holiday cease-fire.
The Syrian Network for Human Rights Wednesday severely criticized the international community for its "weak response" to a report by Human Rights Watch that Syria was using cluster bombs and other prohibited weapons on its people.
SNHR said it documented Monday regime forces used cluster bombs in six areas in four provinces stretching from Daraa in the south to Aleppo in the north. The organization said the bombed areas targeted civilians where forces of the rebel Free Syrian Army were not present.
While SNHR said it held Syria "fully accountable for the use of internationally prohibited weapons," it said the international community and in particular the United Nations "should bear responsibility due to the weak reactions to the consistent reports" of use of banned weaponry by Syria.
The lack of action, the organization said, was a "green light" for Syria to continue violations.
In a separate report, SNHR said it had documented 138 deaths by Syrian forces Wednesday, including one child and two women.
Regime forces killed "tens" of rebel fighters Tuesday, the website for Syria Radio & TV reported.
Several clashes in and around the city of Aleppo resulted in the deaths of "tens of terrorists" and the seizure or destruction of weapons and vehicle, the state-run news agency said.
In Homs, Syrian forces reported they discovered a tunnel that was allegedly used by rebels to smuggle weapons and ammunition. They also reported seizing a workshop in which explosives were made.