American and Russian officials were holding high-stakes talks Monday about the build-up of troops near Ukraine's border, as fears mount over a possible Russian invasion.

US Deputy Secretary of State Wendy Sherman and Russian Deputy Foreign Minister Sergey Ryabkov began their meeting on Monday morning in Geneva, Switzerland, after holding a working dinner on Sunday evening.

The talks follow months of tension near the Ukraine-Russia frontier, where tens of thousands of Russian soldiers have massed.

Deputy National Security Adviser Jon Finer told CNN's Jim Sciutto on Monday that he does not "see a situation in which the US walks away" from talks with Russia, even if Kremlin officials take positions during this week's discussions that are considered nonstarters by the US.