Lakhdar Brahimi told reporters in Cairo that most opposition factions had also said they would observe any ceasefire.
The government said it would make its final decision on Thursday.
Lakhdar Brahimi said he hoped to use the lull in fighting over Eid al-Adha, which starts on Friday, to “discuss a longer and more effective ceasefire”.
Eid al-Adha, the Festival of the Sacrifice, is celebrated by Muslims to commemorate the willingness of Abraham to sacrifice his son Ishmael as proof of obedience to God.
Lakhdar Brahimi has travelled across the Middle East over the past two weeks in an effort to persuade the Syrian government and opposition, as well as their respective backers, to agree to his proposal for a ceasefire to “allow a political process to develop”.
After holding talks on Wednesday with the Arab League’s Secretary General, Nabil al-Arabi, the Algerian diplomat announced that the Syrian government had expressed its support.
“After the visit I made to Damascus, there is agreement from the Syrian government for a ceasefire during the Eid,” he told a news conference.
“Other factions in Syria that we were able to contact – heads of fighting groups – most of them also agree on the principle of the ceasefire.”
Lakhdar Brahimi did not give a precise time period for the truce.
“If this humble initiative succeeds, we hope we can build on it in order to negotiate a longer and more effective halt of military operations, which could be a part of a comprehensive political process,” he added.
The Syrian foreign ministry subsequently issued a statement saying the government’s final decision would be taken on Thursday because the army command was still “studying the cessation of military operations”.
A ceasefire negotiated in April by Lakhdar Brahimi’s predecessor, Kofi Annan, broke down within days and was followed by an escalation in the conflict.
Human rights and opposition activists estimate that more than 30,000 people have been killed since the uprising against President Bashar al-Assad began in March 2011.
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