BEIJING (Reuters) - U.S. 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 was speaking in Beijing, where he and U.S. Trade Representative Robert Lighthizer will hold talks this week, before Chinese Vice Premier Liu He goes to Washington next week for another round of talks in what could be the end game for negotiations.

“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 reporters.

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.

But U.S. officials say privately that an enforcement mechanism for a deal and timelines for lifting tariffs are sticking points.

“Enforceability is key - it’s easy to sign a document if you have no intention of complying with it,” U.S. Agriculture Secretary Sonny Perdue told reporters in Washington, adding that there a few “still lingering” issues that need to be resolved.

“Consequences of lack of compliance need to be very tight in that agreement,” Perdue said.

Chinese officials have also acknowledged that they view the enforcement mechanism as crucial, but say that it must work two ways -- and cannot put restraints only on China.

“There must be guarantees for implementation. This is an important part of the negotiations. We must, to the greatest extent possible, lower and prevent the chances of going back on promises,” one Chinese official close to senior leaders told Reuters.

A second Chinese official with knowledge of the situation said it was too early to say work was in the final stages, but that both sides were “sprinting”.

In Washington, people familiar with the talks say that the question of whether and when U.S. tariffs on $250 billion worth of Chinese goods will be removed will probably be among the last issues to be resolved. Trump has said that he may keep some tariffs on Chinese goods for a “substantial period.”

Erin Ennis, senior vice president of the U.S.-China Business Council, said the deal needs to address U.S. complaints about Chinese theft of intellectual property and forced technology transfers, but it also must resolve tariffs.

“Whatever the resolution is it has got to have a plan of action for the ultimate removal of tariffs, because if it’s an input for a product made in the United States or something a U.S. company ships to China, the tariffs inflate costs and make their products less competitive,” she said.

FILE PHOTO: U.S. Treasury Secretary Steven Mnuchin leaves the G-20 Finance Ministers and Central Bank Governors' meeting at the IMF and World Bank's 2019 Annual Spring Meetings, in Washington, April 12, 2019. REUTERS/James Lawler Duggan

Senator Marco Rubio, a Republican from Florida who has taken a hawkish stance on China trade and security issues, warned that a deal based on Chinese purchases of U.S. agricultural products or a deal that cannot be effectively enforced was unacceptable.

“If you’re not addressing the key industries of the 21st century, in five or 10 years, it’s going to not just going to be a bad deal, it’ll be a catastrophic one,” he said. “They will de-facto dominate those industries.”

U.S. President Donald Trump said on April 4 that a deal might be worked out in about four weeks. Last week, he said he would soon host Chinese President Xi Jinping at the White House. A meeting between the two leaders is 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 were close to finished.

The Chinese government’s top diplomat, State Councillor Wang Yi on Tuesday told a separate group of former U.S. lawmakers that the two countries’ interests were deeply connected.

“In recent months, both countries’ economic and trade teams have held many rounds of high-level consultations and achieved much positive progress,” China’s Foreign Ministry paraphrased Wang as saying.

China hopes that both sides can “work hard, exclude disturbances, and reach a mutually beneficial, win-win agreement,” he added.