"The Russians are thinking," Deshchytsi said, so there is "reason to hope." He reiterated that the new Ukrainian government understands it is vital to establish good relations with all neighbors, including Russia.
Lavrov also spoke by telephone with U.S. Secretary of State John Kerry on Saturday, a U.S. official said on condition of anonymity to describe a private diplomatic conversation.
Kerry "made clear that continued military escalation and provocation in Crimea or elsewhere in Ukraine, along with steps to annex Crimea to Russia would close any available space for diplomacy, and he urged utmost restraint," the official said. Kerry and Lavrov agreed to speak again soon.
Russian President Vladimir Putin has said that Moscow has no intention of annexing Crimea, but that its people have the right to determine the region's status in a referendum.
The Crimean referendum has been denounced by Ukraine's new government. The U.S. moved Thursday to impose its first sanctions on Russians involved in the military occupation of Crimea.
Speaking on the BBC on Saturday, NATO Secretary-General Anders Fogh Rasmussen said that while there is no military response to the recent events of Crimea, the crisis was a reminder of threats to European security and stability.
"I do believe that politicians all over NATO will now rethink the whole thing about investment in security and defense," he told the BBC. "Obviously, defense comes at a cost but insecurity is much more expensive."
An international military mission composed of officers from the U.S. and 28 other nations tried again Saturday to enter Crimea, but it was turned back around the town of Armiansk by armed men.
An AP reporter traveling with the 54 observers from the Organization for Security and Cooperation in Europe said that after the group had stopped, the armed men fired bursts of automatic weapons fire to halt other unidentified vehicles. No injuries were reported.