US Secretary of State Hillary Clinton has warned Moscow of risks in losing influence in the Middle East if it does not act more constructively.
China is also unlikely to back such a move in the UN Security Council.
Meanwhile, the Syrian government has been accused of war crimes and crimes against humanity in a new report by the human rights group, Amnesty International.
Mr Lavrov, who is due to meet UK Foreign Secretary William Hague in Afghanistan on Thursday, has rejected any push for the Annan plan to be enforced under the Chapter Seven provision of the UN charter.
On Wednesday, he told reporters in Tehran that Russia could not disregard what had happened in Libya after the UN charter had been invoked and Nato had "ignored" UN resolutions.
A mistranslation of his remarks threatened to intensify a diplomatic row between Russia and the US on Wednesday, after Iranian media quoted Mr Lavrov as saying that the Americans had provided arms to Syria's rebels. Russia's foreign ministry later pointed out that he had been speaking about US weapons supplies "to the region".
Mrs Clinton has already accused Moscow of sending attack helicopters to Damascus and has urged it to "cut these military ties completely".
Her accusations have been met with outrage by Mr Lavrov, who said his government was completing earlier lawful weapons contracts with Syria for anti-aircraft air defence - not, he added, for use "against peaceful demonstrators... unlike the US, who regularly supply such weapons to the region".
While calling on Moscow to cut its military ties with Damascus, the US secretary of state said that attempts by the US and Russia in recent years to "reset" their relations had been quite constructive. However, she said, they disagreed on Syria.
"It's not the only issue we disagree on, but it is one where people are being killed every single day, where violence is escalating," she said.
Mrs Clinton said the situation was "spiralling toward civil war", stopping short of the earlier remarks of French Foreign Minister Laurent Fabius who said that Syria was already in civil war.