Brahimi's push to get Assad and rebels seeking to topple him to stop fighting for the four-day Eid al-Adha feast set to begin Oct. 26 reflects how little progress international diplomacy has made in halting 19 months of deadly violence in Syria. Activists say more than 33,000 people have been killed.
Unlike his predecessor as joint U.N.-Arab League envoy, Kofi Annan, Brahimi has said he has no grand plan to end Syria's civil war. Instead, he presented the truce as a "microscopic" step that would alleviate Syrian sorrow temporarily and provide the basis for a longer truce.
Even a short-term cease-fire faced hurdles. Both sides in the past have verbally signed on to cease-fires only to then blatantly disregard them. And before Brahimi spoke, Syria's government dismissed the plan, saying the rebels lack a unified leadership to sign the truce.
"There is the state, represented by the government and the army on one front, but who is on the other front?" asked an editorial in the Al-Thawra daily.
The scores of rebel units fighting a brutal civil war against the regime have no single leader, and many don't communicate with each other.
Brahimi spoke following meetings with top Lebanese officials as part of a regional tour. He said all countries must work to stop the bloodshed by halting arms shipments so the conflict doesn't spread.
Turkey, Saudi Arabia and Qatar are sympathetic to the rebels and are believed to be facilitating their acquisition of weapons or arming them directly. Iran and Russia are Assad's biggest supporters and provide the Syrian military with most of its advanced weaponry.
"These countries need to realize, as we heard today in Lebanon, that it is not possible that this crisis will stay inside Syrian border forever," Brahimi said. "Either it has to be taken care of or it will spread and spill over and consume everything."
Rebel leaders were not immediately available for comment on the proposed truce.
Syrian Foreign Ministry spokesman Jihad Makdessi said the government was waiting for Brahimi to come to Damascus to brief officials there on the results of his tour. The regime would welcome any "constructive initiative," Makdessi said in statement released Wednesday by the state news agency.
It was unclear whether Brahimi would travel to Damascus from Beirut.
Turkish Foreign Minister Ahmet Davutolgu said his country supports a holiday cease-fire but was skeptical that it would lead to a longer truce without an international force to make it "sustainable."
"A cease-fire can be declared but the international community would need to take certain measures for its sustainability," the state-run Anadolu agency quoted him as saying.
Davutolgu later told reporters in Ankara that "for a true cease-fire to hold, the siege of the cities, their bombings by air and by tanks must immediately stop."
Inside Syria, activists reported clashes in the northern provinces of Idlib and Aleppo as well as outside of the capital, Damascus.
Amateur videos posted online showed what rebels said was a helicopter shot down by rebel fire near the northern town of Maaret al-Numan. Fighting has been raging in the area since rebels took the town last week.
One video shows a white helicopter spiraling as it falls through the sky, leaving a trail of smoke behind before bursting into flames. Rebels on the ground can be heard chanting "God is great!"
An activist in the area who said he saw the explosions said the helicopter was likely hit with anti-aircraft guns rebels have captured from regime forces and sometimes mounted on the backs of trucks.
He said the regime has been bombing villages in the area for more than a week and had destroyed many homes.
"The planes are hitting us as revenge," said the activist, who gave his name as Qais al-Idlibi. "They can't make progress on the ground, so they are hitting us from the air."
He said the remaining civilians sleep outside in fields for fear of airstrikes, and the shooting boosted their morale.
The Britain-based Syrian Observatory for Human Rights also reported the helicopter downing, saying the debris fell in the village of Baseeda.
The activists' claims and videos could not be independently verified.
The rebels have previously claimed in videos posted on the Internet to have downed government aircraft, although opposition commanders insist their weapons are no match for the regime's airpower.
French Foreign Minister Laurent Fabius told reporters on Wednesday that at least some rebels now have heavier weapons, which have recently forced military aircraft "to fly very high." Speaking in Paris ahead of a meeting on aid to Syria, Fabius said Assad's warplanes are dropping so-called barrel bombs and cluster bombs on rebel-held areas.
Barrel bombs are makeshift weapons consisting of containers stuffed with TNT. Earlier this month, Syrian refugees said their villages in the central Homs province had come under heavy air attack from barrel bombs.
Human Rights Watch on Sunday cited allegations that Assad's government has been using cluster bombs indiscriminate scattershot munitions which are banned by most nations basing its conclusions on amateur video and testimony from the front lines.
The Syrian military has denied using such bombs.
The civil war has displaced more than 1 million Syrians inside the country and sent hundreds of thousands more over the borders to seek refuge in neighboring nations.
On Wednesday, U.N. humanitarian chief Valerie Amos said more than half of Syria's health facilities have been destroyed or damaged in the war and many children are not getting vaccinated or going to school. She also expressed concern over those near Syria's borders who have not been allowed to leave the country.
Syria's state-run news agency criticized the European Union for imposing additional sanctions against Damascus as "unjustified" measures that have "no legal or moral basis as they contradict international law."
The E.U. on Monday increased pressure on Assad's regime, prohibiting the provision of any financial services to Syrian arms exports, banning the country's national carrier from the 27-member bloc's airports. It also added 28 people to those whose assets are frozen and who are denied E.U. visas.
A ban on Syrian cargo flights is already in place, as is an obligation for E.U. countries to inspect ships or planes suspected of carrying arms to Syria.