The partial trade agreement between the U.S. and China has caused relief among officials in Beijing, one of President Donald Trump's outside advisors told CNBC on Monday.
"I think that may have scared the Chinese that they were going to get into a serious trade war with access to our capital markets being cut off, among other things," Pillsbury said. "These are very scary options. Obviously, that's off the table now in the sense that there's been so much substantial progress on Friday, there's no need to think about escalation options at this time."
Officials from the U.S. and China said Friday they struck an agreement on the first part of a deal to end the long-running trade dispute between the world's two largest economies.
The deal, which hasn't been officially signed, is said to include a pledge from China to buy more U.S. agricultural products and address some concerns over intellectual property. The U.S., in return, agreed to suspend a tariff hike planned for this week.
On Monday, CNBC reported that Chinese officials want another round of discussions before signing the "phase one" deal.
In addition to the principal agreement on agricultural purchases, Pillsbury said the part of the deal that would establish a "large office in both Washington and Beijing that would try to adjudicate disputes before they go to enforcement action" was another sign of progress.
"I think it's wrong to say there's no progress, but it's also wrong to say there's a final deal, open the champagne cork," Pillsbury said.
Treasury Secretary Steven Mnuchin told CNBC on Monday that he expects to have an agreement in place by mid-December, when another round of tariffs on Chinese goods is set to go into effect.
"I have every expectation if there's not a deal those tariffs would go in place, but I expect we'll have a deal," Mnuchin said on "Squawk Box."