Trump expressed his thanks for the greetings and asked Liu to convey their greetings to Xi and Peng.
Trump made the comments at an event on opioid abuse.
Trident Seafoods has already sent a team with Alaska Governor Bill Walker's trade mission to China, which began on May 26, to explore more business opportunities.
Trump and Abe are expected to determine the direction of the trade talks at their meeting on the sidelines of the G20 Summit in Osaka in June.
Trump's comments came as he eyes another cabinet shakeup.
Trump spoke to reporters as he departed for a trip to hurricane-ravaged Puerto Rico. He called the gunman "demented" and said "we're looking into him very seriously", the Associated Press reported on Tuesday.
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Trump's job approval rating stood at 41 percent in the week that ended on July 8, down from his highest 45 percent registered in the week ended on June 17, according to Gallup.
Trump called the shootings "domestic terrorism" and directed the FBI to devote more investigative efforts and psychological profiling to prevent future attacks.
Trump goes after Fauci, tries to buck up his campaign team - World - Chinadaily.com.cn
Trump said he will meet at the White House on Monday with representatives of major drug companies about speeding up development of a vaccine. "We are having very good initial feedback "about a vaccine, he said.