At a separate news conference at the Russian ambassador's house, Lavrov did not address the troop issue. Instead, he made the case for Moscow's idea of Ukraine as a federalized nation with its various regions enjoying major autonomy from the government in Kiev.
Russia says it is particularly concerned about the treatment of ethnic Russians and Russian speakers who live in southern and eastern Ukraine.
Lavrov said that Ukraine can't function as a "unified state" and should be a loose federation of regions that are each allowed to choose their own economic, financial, social, linguistic and religious models.
He said every time Ukraine has elected a new president, the country has adopted a new constitution, proving that "the model of a unified state doesn't work."
Ukrainian officials are wary of decentralizing power, fearing that pro-Russia regions would hamper its Western aspirations and potentially split the country apart. However, they are exploring political reforms that could grant more authority to local governments.
The US has been coy about their position on a federation. Washington has encouraged ongoing political and constitutional reform efforts that the government in Kiev is now working on but US officials insist that any changes to Ukraine's governing structure must be acceptable to the Ukrainians.
Kerry said the federation idea had not been discussed in any serious way during his meeting with Lavrov "because it would have been inappropriate to do so without Ukrainian input."
"It is not up to us to make any decision or agreement regarding federalization," he said. "It is up to Ukrainians."
"We will not accept a path forward where the legitimate government of Ukraine is not at the table," Kerry said, adding that the bottom line is: "No decisions about Ukraine without Ukraine."
Lavrov denied that Moscow wants to "split Ukraine."
