"We all want Syria democratic, united, secular; Syria which is a home for all ethnic and confessional groups, whose rights are guaranteed," Lavrov said. "But we have some differences as for the details on how to get there."
"But we agreed on some steps which we will undertake very soon…"
Lavrov also said that he and Kerry discussed the importance of coordination between the US and Russian military to avoid unintended incidents in Syrian airspace.
"The first instruction to us was to make sure that the military of the United States – the coalition led by the United States on the one hand – and the military of the Russian Federation – now engaged in some operations at the request of the Syrian government – get in touch and establish channels of communication to avoid any unintended incidents,” he said.
Kerry described the meeting as "constructive," and stated Washington's concern about the targets of the Russian airstrikes.
"We agreed on the imperative…of having a military-to-military deconfliction meeting," Kerry said.
"We also agreed that it is imperative to find a solution to this conflict and to avoid escalating it in any way or seeing it intensified by forces beyond anybody's control," he added.
Moscow began conducting airstrikes against the self-proclaimed Islamic State terrorist group on Wednesday, carrying out roughly 20 operations.
"As a result of airstrikes, ammunition and fuel depots, heavy military hardware, as well as command posts in the mountainous areas have been destroyed," Russian Defense Ministry spokesman Maj. Gen. Igor Konashenkov said in a statement.
While US officials have expressed concern that Russian airstrikes are not targeting the Islamic State, Lavrov dismissed those claims.
"Our air force works in Syria in coordination with the Syrian army and exclusively on targets connected to IS," he stressed. "There were rumors that some civilians were injured as a result of the strikes, we have no such information. We are monitoring the situation very closely in order to ensure the precision of the strikes."
Lavrov also cautioned against Western demands for Assad's resignation.
"I think that life has proved that it is not realistic to demand in ultimatum the departure of a president in a situation when there is such a crisis in the country [Syria]," he said. "It is necessary to negotiate."