Walid al-Moallem, who was in Moscow to discuss Syria's civil war with Russian officials, did not say whether the rebels would first have to lay down their arms before Damascus would agree to sit with them at the negotiating table.
Still, the offer marked the first time that a high-ranking Syrian official has stated publicly that the government would meet with opposition fighters.
"We're ready for a dialogue with anyone who's willing for it," al-Moallem said. "Even with those who carry arms. We are confident that reforms will come about not with the help of bloodshed but through dialogue."
Syria's 23-month-old conflict, which has killed more than 70,000 people and destroyed many of the country's cities, has repeatedly confounded international efforts to bring the parties together to end the bloodshed. Russia, a close Assad ally and his regime's chief advocate on the international stage, offered last Wednesday to broker talks in concert with the Arab League between the rebels and the government.
The proposal -- which the Kremlin would be unlikely to float publicly without first securing Damascus' word that it would indeed take part -- suggested the regime could be warming to the idea of a settlement as it struggles to hold territory and claw back ground it has lost to the rebels.
Ahead of the meeting with al-Moallem on Monday, Lavrov reiterated his call for Damascus to negotiate with the opposition, saying that "the situation in Syria is at a crossroads now." He also warned that further fighting could lead to "the break-up of the Syrian state."
Past government offers for talks with the opposition have included a host of conditions, such as for the rebels to first lay down their weapons. Those proposals have been swiftly rejected by both activists outside the country as well as rebels on the ground.
The prospect of negotiating with the armed opposition is made all the more difficult by the fractured state of those fighting to topple the regime -- there are dozens of brigades and groups across the country and no unified command.
The head of one group, Free Syrian Army chief Gen. Salim Idriss, said he is "ready to take part in dialogue within specific frameworks," but then rattled off several conditions that the regime has flatly rejected in the past.
"There needs to be a clear decision on the resignation of the head of the criminal gang Bashar Assad and for those who participated in the killing of the Syrian people to be put on trial," Idriss told pan-Arab Al-Arabiya TV.
He said the government must agree to stop all kinds of violence and to hand over power, saying that "as rebels, this is our bottom line."
Both sides in the conflict in recent weeks have floated offers and counter offers to hold talks aimed at resolving the crisis.
In a speech in January, Assad offered to lead a national dialogue to end the bloodshed, but also said he would not talk with the armed opposition and vowed to keep on fighting. The opposition rejected the proposal.
This month, the leader of the Syrian National Coalition, the umbrella group for opposition parties, said he would be open to discussions with the regime that could pave the way for Assad's departure, but that they government must first release tens of thousands of detainees. The government refused.
Speaking to reporters Monday in Cairo, Mouaz al-Khatib accused the regime of procrastinating and said it had derailed the opposition's dialogue offer by not responding to its conditions.
"We are always open to initiatives that stop the killing and destruction but the regime rejected the simplest of humanitarian conditions. We have asked that the regime start by releasing women prisoners and there was no response," he said. "This regime must understand that the Syrian people do not want it anymore."
Lucas reported from Beirut. Associated Press writer Zeina Karam in Beirut contributed to this report.