While he would not name the countries, Lavrov said Russia had responded by telling them to go directly to the Syrian leader.
"If there is anyone willing to provide him guarantees, they are welcome!" Lavrov said on board a plane returning from Brussels, where he attended a Russia-EU summit.
"We would be the first to cross ourselves and say: "Thank God, the carnage is over! If it indeed ends the carnage, which is far from certain."
Syria's conflict started in March last year as an uprising against Assad, whose family has ruled the country for four decades. But the bloody crackdown that followed led rebels to take up arms, and the ensuing fighting transformed into a civil war.
The regime has come under added condemnation in recent weeks as Western officials raise concerns Assad might use chemical weapons against rebels in an act of desperation.
Syria refuses to confirm or deny if it has such weapons but is believed to have nerve agents as well as mustard gas. It also possesses Scud missiles capable of delivering them.
Lavrov said the Syrian government has pulled its chemical weapons together to one or two locations from several arsenals across the country to keep them safe amid the rebel onslaught.
"According to the information we have, as well as the data of the U.S. and European special services, the government is doing everything to secure it," he said. "The Syrian government has concentrated the stockpiles in one or two centers, unlike the past when they were scattered across the country."
Lavrov added that U.N.-Arab League peace envoy for Syria, Lakhdar Brahimi, would visit Moscow for talks before the year's end.
The conflict's sectarian dimension looked set to deepen at the weekend, as rebels threated to storm two predominantly Christian towns in a central region if residents do not "evict" government troops they say are using the towns as a base to attack nearby areas.
A video released by rebels showed Rashid Abul-Fidaa, who identified himself as the commander of the Ansar Brigade for Hama province, calling on locals in Mahrada and Sqailbiyeh to rise up against Assad's forces or prepare for an assault.
"You should perform your duty by evicting Assad's gangs," said Abdul-Fidaa, who wore an Islamic headband and was surrounded by gunmen. "Otherwise our warriors will storm the hideouts of the Assad gangs."
He also accused regime forces of taking positions in the two towns in order to "incite sectarian strife" between Christians and the predominantly Sunni opposition. Assad belongs to the Alawite minority sect, an off-shoot of Shiite Islam.
The threat comes just two days after a U.N. team investigating human rights abuses in Syria accused anti-Assad militants of hiding among the civilian population, triggering strikes by government artillery and the air force.
The Britain-based Syrian Observatory for Human Rights, the activist group which reported the rebel ultimatum on Saturday, said such an attack by rebels could force thousands of Christians from their homes.
Christians, who make up about 10 percent of Syria's population, say they are particularly vulnerable to the violence sweeping the country of 22 million people. They are fearful that Syria will become another Iraq, with Christians caught in the crossfire between rival Islamic groups.
Clashes between troops and rebels in the central city of Homs, Syria's third largest, have already displaced tens of thousands of Christians, most of whom either fled to the relatively safe coastal areas or to neighboring Lebanon.
Rami Abdul-Rahman, who heads the Observatory, said some Christians and Alawites have also left Hama province in the past several days to escape violence. He said some of them found shelter in the coastal city of Tartus.
In Damascus, the new head of the Greek Orthodox Church of Antioch said that Christians in Syria had deep roots in the country and were not part of the conflict. Speaking to reporters in Damascus, Patriarch John X. Yazigi urged rival factions to negotiate a settlement.
Violence continued unabated on Saturday, particularly in the capital.
The Observatory said a car bomb went off in the Damascus neighborhood of Qaboun, killing at least five people and wounding others. A Syrian official confirmed the blast but had no immediate comment regarding casualties.
Elsewhere, the Syrian army said in a statement carried on state-run TV that it had repelled a rebel attack on a military base that killed a regimental commander in the Damascus suburb of Chebaa.
Also in Damascus, the state-run news agency SANA said gunmen assassinated a cameraman for the government's TV station, the latest such killing in recent months.
In another development, 11 rebel groups said they have formed a new coalition, the Syrian Islamic Front.
A statement issued by the new group, dated Dec. 21 and posted on a militant website Saturday, described it as "a comprehensive Islamic front that adopts Islam as a religion, doctrine, approach and conduct."
Several rebel groups have declared their own coalitions in Syria, including one calling itself an "Islamic state" in the embattled northern city of Aleppo.
The statement said the new group will work to avoid differences or disputes with the other Islamic groups.
- AP
