Trump said in a tweet on November 1 that he had "a long and very good conversation" with Xi, offering some hope that trade tensions may cool after the G20 meeting.
The two countries already have imposed tariffs on hundreds of billions of dollars of each other's goods and Trump has threatened to slap tariffs on the remainder of China's $500 billion-plus exports to the United States if the disputes can not be resolved.
President Trump says his discussions with his Chinese counterpart are moving along "nicely" ahead of their planned meeting at the G-20 in Buenos Aires at the end of the month.
The news agency said it was not clear if Trump was easing up on demands that China has resisted, and it cited one person as saying intellectual property theft was a sticking point on a possible deal.
The telephone conversation on Thursday was Trump and Xi's first publicly disclosed call in six months. "China would love to make a deal", Trump told Breitbart at the time.
The U.S. president said Wednesday that he'd like to sit down and make a "fair deal" with China on trade that would eliminate the need for the massive tariffs he's put on the nation.
Jacob Parker, vice president of China operations at the U.S. "We don't know what the tariff rate might be", he said.
Trump said he and Xi plan to meet during a gathering of the Group of 20 major economies this month in Argentina.
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Despite the promise offered by the Trump-Xi telephone call, the level of tension between the two nations was demonstrated just hours after it ended when the U.S. filed charges against Chinese technology firm Fujian Jinhua Integrated Circuit Co and its Taiwanese partner.
President Trump has made very clear to China that they must change their "unfair" trade practices including theft of US intellectual property.
Kudlow said Thursday at an event in Washington that Trump and Xi might be able to break the logjam on issues during the summit.
Hours later, however, the US Justice Department accused another Chinese firm of unfair practices, part of an across-the-board pressure campaign by the Trump administration targeting China.
The United States has imposed tariffs on $250 billion worth of Chinese goods so far, while China has retaliated with $110 billion worth of tariffs on USA goods. "If President Trump makes an agreement with President Xi, there is nobody above them to overturn it", he said.
Kudlow believes China is getting isolated in the ongoing trade war, as the United States, Japan, and the European Union officials met in September in NY on the sidelines of the U.N. General Assembly and reached a deal to tackle China's unfair trade practices.
Trump's posture toward China has been closely watched by investors, who are looking for the possibility of tensions cooling.