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.
Mr 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.
Mr 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 reporters.
“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.”
Mr Brahimi did not say when he believed the truce would begin or how long it would last.
“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 said the government would announce its “final position on the issue” on Thursday.
“The proposal to halt military operations during the blessed Eid al-Adha holiday is still being studied by the leadership of the army and the armed forces,” a statement explained.
Gen Mustafa al-Sheikh, head of the rebel Free Syrian Army’s military council, said any ceasefire observed by the government would be reciprocated, but warned that it had “lied many times before”.
“It is impossible that the regime will implement the truce, even if it says it will,” he told the AFP news agency.
The leader of the Syrian National Council, the main opposition coalition, told the Associated Press he had little hope the truce would take hold.
“This regime, we don’t trust it, because it is saying something and doing something else on the ground,” Abdelbaset Sayda added.
Earlier this week the UN’s head of peacekeeping operations, Herve Ladsous, revealed he had started to make plans to send an observer force to Syria should a lasting ceasefire be agreed.
A ceasefire negotiated in April by Mr Brahimi’s predecessor, Kofi Annan, broke down within days despite the presence of unarmed UN monitors, and was followed by a dramatic escalation in the conflict.
Mr Brahimi’s announcement came as violence was reported in and around Damascus, and in the north of the country.
The Syrian Observatory for Human Rights, a UK-based activist group, said at least 48 people had been killed nationwide on Wednesday, including 16 civilians in Douma, a north-western suburb of the capital.
Eight soldiers also died in a car bombing in Raqqa province, it added.
In Moscow, the Chief of the General Staff of the Russian armed forces, Gen Nikolai Makarov, said the Syrian rebels had been given shoulder-launched surface-to-air missile systems, including US-made Stingers.