U.S. Treasury Secretary Steven Mnuchin said that he hopes to make "substantial progress" with Chinese negotiators in the next two rounds of trade talks, as the world's two largest economies look for ways to end their bruising trade war.

Mnuchin and U.S. Trade Representative Robert Lighthizer are in Beijing this week for the latest negotiations in what could be the talks' end game. Chinese Vice Premier Liu He will go to Washington for another round of talks scheduled for next week.

"We've a meeting here, and then the vice premier and team will be coming back to Washington D.C., and we hope to make substantial progress in these two meetings," Mnuchin told.

"I'm not going to comment on specific issues of the discussions," Mnuchin said. "They've been quite broad as I've said before. We've made a lot of progress. We look forward to the meetings here."