It said Kiev's plans to reform its constitution and transfer more power from the central government to regional authorities must be inclusive, transparent and accountable — including through the creation of a broad national dialogue.
Speaking at a separate news conference, Lavrov said the OSCE mission "should play a leading role" moving forward.
Earlier, Russian President Vladimir Putin criticized the U.S. and its European allies for having what he called a double standard concerning Ukraine and said he hoped he would not have to deploy troops to Ukraine.
But he also seemed to keep the door open for Russia to recognize Ukraine's presidential election set for May 25, softening his previous demand that it must be postponed until the fall and preceded by a referendum on broader powers for the regions.
Ukraine was hoping to use the Geneva talks — the first of their kind over the crisis that threatens the new government in Kiev — to placate Russia and calm hostilities with its neighbor even as the U.S. prepared a new round of sanctions to punish Moscow for what it regards as fomenting unrest.
Meanwhile, Russia was honing a strategy of its own: Push the West as far as possible without provoking crippling sanctions against its own financial and energy sectors or a military confrontation with NATO.
In a television appearance in Moscow on Thursday, Putin denied claims that Russian special forces were provoking unrest in eastern Ukraine. He called the Ukrainian government's effort to quash the unrest a "crime."
In Washington, Defense Secretary Chuck Hagel said the U.S. would send non-lethal assistance to Ukraine's military in light of what he called Russia's ongoing destabilizing actions there. He told a Pentagon news conference that the military assistance to Ukraine will include medical supplies, helmets, water purification units and power generators.