"We will make that happen," he added.
Lavrov had earlier Saturday held talks with US Vice President Joe Biden and UN-Arab League envoy Lakhdar Brahimi amid strong disagreement between Moscow and Washington about ways to end the 22-month Syria conflict, which has claimed upwards of 60,000 lives, according to the United Nations.
Khatib, who became the head of the coalition late last year, reiterated on the opening day of the Munich talks Friday an earlier surprise announcement that his group was ready for dialogue with the Damascus regime -- subject to conditions including the release of 160,000 detainees.
Lavrov said Moscow "welcomed" the initiative, adding: "If we take into account the fact that the coalition was founded on a refusal to engage in a dialogue with the regime, it's a very important step."
Biden, in his meeting with Lavrov, called on Washington and Moscow to put aside "serious differences" stressing the need for US-Russian cooperation, including over Syria, the White House said.
Biden met Khatib and Brahimi in Munich too.
Biden "urged Khatib to continue his efforts to maintain unity among the SOC (Syrian Opposition Coalition) leadership, to isolate extremist elements within the broader opposition, and to reach out to, and be inclusive of, a broad range of communities inside Syria, including Alawites, Christians and Kurds," according to a White House statement.
Earlier the US vice president told the conference that the United States and its partners were pushing to help the Syrian opposition become "more inclusive and cohesive", insisting Assad was a "tyrant" and must go.
The United States and its allies have made repeated calls for Assad's ouster, while key Damascus ally Russia has resisted any international action.
Lavrov, whose country has blocked three UN Security Council resolutions sanctioning Assad for the violence, called for another meeting of the Syrian action group led by Brahimi in a bid to find an accord on a transition, saying he believed progress was possible.
Russia's top diplomat also said Moscow shared Washington's concern about the possible use of chemical weapons in Syria.
"We coordinate this issue with the Americans on a daily basis. We have reliable information that for now, the Syrian government has control of the chemical weapons, that the situation is safe," Lavrov said in his address to the conference.
"I think that this (the use of chemical weapons) is a 'red line' for everyone. We are categorically against the use of any arms."
In a dramatic development last week, Syria said Israeli air strikes hit a weapons research centre near Damascus and threatened to retaliate.
Israel has not commented on the reports, but a US official said an Israeli raid struck surface-to-air missiles and a nearby military complex on the capital's outskirts.
Israel has frequently warned that if Syrian chemical weapons fall into the hands of the Shiite movement Hezbollah, its arch-foe and close Damascus ally, this would be a casus belli.
US Defence Secretary Leon Panetta told AFP that Washington is also concerned the "chaos" in Syria could allow Hezbollah to obtain sophisticated weaponry.
On the ground on Saturday, rebels were reported to have taken control of the Sheikh Said district of Aleppo, Syria's second city, in a strategic victory securing a key route to its international airport.
The Syrian Observatory for Human Rights, which relies on activists and medics on the ground for its information, said at least 114 people were killed on Saturday: 46 civilians, 33 rebels and 35 soldiers.
Meanwhile, a senior Iranian official visiting Damascus reiterated that his country stood squarely behind the Syrian regime.