US Treasury Secretary Steven Mnuchin said on Tuesday 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 US 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 DC, and we hope to make substantial progress in these two meetings," Mnuchin told reporters at a hotel in Beijing.

Beijing and Washington have cited progress on issues including intellectual property and forced technology transfer to help end a conflict marked by tit-for-tat tariffs that have cost both sides billions of dollars, disrupted supply chains and roiled financial markets.

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

US President Donald Trump said on April 4 that the two sides could have a deal worked out in about four weeks. Last week, he said he would soon host Chinese President Xi Jinping at the White House - a meeting seen as needed to cement an agreement.

Mnuchin, speaking to Fox Business Network in an interview that aired on Monday, said the trade negotiations aimed at enforcement is close to finished.

Agreeing to a way to enforce a deal is one thing. Ensuring it holds up under ties strained by growing mistrust and geopolitical tensions will be another, people say.