"The only way [US-Russia cooperation] can be productive though, is for Russia to acknowledge that Assad is part of the problem," Corker said on Tuesday.
Whether the United States and Russia, Corker noted, can reach an agreement about the Assad government "is a big issue."
"And yet, I think there is a possibility that could be the case," he asserted.
The United States and Russia have "the same concerns" about terrorism, and counterterrorism is an area where "candidly, I always thought there was a mutuality of interest," Corker explained.
On Saturday, a group of nations including the United States and Russia reached an agreement in Vienna establishing a timetable for a Syrian peace agreement, including a call for new Syrian elections by May 2017.