Appearing on CBS News' Face the Nation, Bárcena would only say that she expects the lack of tariffs and the ratification of a new North American trade agreement would ultimately result in more USA goods being imported to Mexico.
"If we didn't have [the threat of] tariffs, we wouldn't have made a deal with Mexico", Trump said.
Trump is buoyed by his self-declared victory following a days-long battle with Mexico after he threatened to impose tariffs unless Mexican authorities did more to stem the migrant flow to their shared border.
"China is going to make a deal because they're going to have to make a deal", he added.
In an interview on CNBC on June 10, Trump said that proposed tariffs on $300 billion worth of Chinese goods would immediately be imposed in the event that the two leaders do not meet. "They devalue. They loosen" monetary policy to help offset the burden of tariffs, he said.
When the U.S. president manages to get some concessions from foreign partners, he "lies and exaggerates what was achieved" in order to impress voters at home, the economist said, adding that Trump wants to demonstrate that he is "tough" on foreign governments. "We have noted that the U.S. publicly stated many times that it looks forward to arranging a meeting between the Chinese and USA presidents on the sidelines of the G-20 summit". They take advantage of us in every way possible and the U.S. Chamber is right there with them. That heavily-qualified denial doesn't convey much confidence, though, and the fact that Xi felt compelled to defend the strength of his country's economy during an interview with Chinese and Russian media shortly before meeting with Putin only makes Xi's braggadocio seem even more contrived.
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Trump also complained that even though he selected four of the Fed's five board members, including elevating Jerome Powell to chairman, "We have people on the Fed that really weren't, you know, they're not my people".
He said he believes the situation brought about by tariffs will force the Chinese government to the negotiating table to make a deal with the US.
"If we do, that's fine and if we don't, that's fine", Trump said.
Trump again hinted that part of the deal he struck with Mexico is not yet public. But the USA delegation left without any significant breakthrough on China.
Asked if a failure by Xi to come to the summit would lead to tariffs kicking in on a further $300 billion in Chinese imports, Trump told CNBC television: "Yes it would". "And if there's no meeting between the two leaders, Trump will put the blame on China", said Zhou Xiaoming, a former Mofcom official and diplomat.
Trump has touted the migration agreement he struck with Mexico last week as a sign of his deal-making acumen.
The United States has already imposed 25% tariffs on $250 billion worth of goods.
The high tariffs on Chinese goods by the USA will weaken firms in such sectors, which will not be able to import products from other developing countries.