The Chinese have not acknowledged a 90-day deadline for the talks or said that they plan to "immediately" increase purchases of USA farm goods.
According to details released by the White House, Trump agreed to postpone a planned January 1 escalation of tariffs on Chinese goods for 90 days, while Xi agreed to buy more American agricultural goods in the meantime.
In addition, Treasury Secretary Steven Mnuchin said on Tuesday on the Fox Business Network that China agreed to buy $1.2 trillion of US products.
USA negotiators have a list of 142 requirements that China has to agree to before it enters into a trade deal.
Trump says he wants to de-escalate trade tensions with China but insists on Beijing addressing long-standing issues such as intellectual property theft, forced technology transfers, and tariffs and nontariff barriers.
"When people or countries come in to raid the great wealth of our Nation, I want them to pay for the privilege of doing so".
Trump, via Twitter, held out the possibility of an extension of the ceasefire but warned tariffs would be back on the table if the talks failed to bear fruit.
Mr Pompeo said in Brussels on Tuesday that the United States could abandon some global agreements to thwart bad actors like China, which he accused of cynically exploiting World Trade Organisation rules.
"China will start with the implementation of the specific matters in which consensus has been reached, the sooner the better", it added, without providing more details.
Following these tweets, Trump advisors like Treasury Secretary Steve Mnuchin and top economic adviser Larry Kudlow were left to lower expectations and admit that while a number of issues had been discussed between the two sides, essentially no actual agreements had been reached.
Trump has exaggerated the effect of the tariffs on US revenue.
While he said he would "happily sign" a fair deal that addresses U.S. concerns, he warned: "remember, I am a Tariff Man". But Mnuchin added, "If that's real" - thereby raising some doubt - it would close the U.S. trade deficit with China, and added: "We have to have a negotiated agreement and have this on paper".
He also said that China's vice premier, Liu He, had told him there would be changes made "immediately" to show the Chinese were serious about a new agreement. The Dow finished the day just a hair over 25,000 points-meaning that the stock market has been basically flat since March 1, when Trump announced the first round of tariffs and the Dow was sitting at 24,600 points.
One of the few automotive stocks to score a gain on Tuesday was Tesla which only recently began work on a new factory in Shanghai that eventually will let it sidestep the tariff battle.
The ministry lauded Mr Trump's talks with President Xi Jinping at the weekend as "successful", and said it was "confident" their agreement would be implemented.
"Narrow agreements and modest concessions in the ongoing trade dispute will not bridge the wide gulf in their respective economic, political and strategic interests", Moody's Investors Service said in a report that predicted U.S.
China pledged to buy more from the USA, and the White House said the two sides would negotiate "structural changes" to thorny issues plaguing relations, though few details and no dollar amounts were disclosed.