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Speaking to Russian news agencies, Mr Lavrov criticised Kyiv's approach to the talks.
"Good will has its limits but if it isn't reciprocal, that doesn't help the negotiation process," he said.
"But we are continuing to engage in negotiations with the team delegated by [Ukrainian President Volodymyr] Zelenskyy, and these contacts will go on."
But Mr Lavrov accused former actor Mr Zelenskyy of pretending to negotiate.
"He's a good actor," he said. "If you watch attentively and read attentively what he says, you'll find a thousand contradictions."
Given the current tension, Mr Lavrov said the chances of a Third World War were genuine.
"The danger is serious, it is real, you can't underestimate it," he told the Interfax news agency.
But Mr Lavrov said he was confident that "everything will, of course, finish with the signing of an accord".
"But the parameters of this accord will be defined by the state of the fighting that will have taken place at the moment the accord becomes reality," he said.
His comments regarding the risk of a third World War were later dismissed by the UK's Armed Forces minister James Heappey, who described Mr Lavrov's position as "bravado".