The two world leaders met last night for a dinner meeting to discuss trade at the sidelines of the Group of 20 leaders' summit.
"This was an incredible and productive meeting with unlimited possibilities for both the United States and China", Trump said in the statement.
However the USA trade representative, Robert Lighthizer, said he would be surprised if Mr Trump's working dinner with Mr Xi "wasn't a success".
As part of the detente, Trump agreed to delay plans to raise tariffs on $200 billion in Chinese goods that would have taken effect January 1.
Mike Starkey offloads soybeans from his combine as he harvests his crops in Brownsburg, Indiana, Sept. 21, 2018.
The Chinese leader also said he was "saddened by the passing away of President Bush who had made an important contribution to the China-U.S. friendship and relationship during his lifetime". "It will have an incredibly positive impact on farming, meaning agriculture, industrial products, computers, every type of product".
Sanders said the two leaders had agreed to begin immediate negotiations on "structural changes" on chronic issues of contention, including the practice of forcing USA investors to hand over technological knowhow, intellectual property protection and non-tariff barriers to entry for United States businesses. The planned tariff increase would be paused in the meantime, but she stressed the tariffs will be raised to 25 percent at the end of 90 days if "the parties are unable to reach an agreement".
The Trump administration has taken a tougher tone against Beijing, stating that the United States is prepared to more than double its tariffs on Chinese goods if they fail to reach a deal.
Some of the details were echoed by Chinese Foreign Minister Wang Yi, who confirmed that both countries will step up negotiations. Most of the USA supply of the drug is made in China.
The new designation for the synthetic opioid drug means people in China who sell fentanyl to the United States "will be subject to China's maximum penalty under the law", according to a statement from the White House.
The White House statement called the meeting "highly successful".
High-stakes trade talks between U.S. President Donald Trump and Chinese President Xi Jinping on Saturday went "very well", a top White House aide said, suggesting there may have been progress toward defusing the two countries' damaging tariffs war.
"The two presidents agreed that the two sides can and must get bilateral relations right", Wang said, per Reuters.
Xi added, "Only with cooperation between us can we serve the interest of world peace and prosperity".
In other key results from the talks, the USA promised to uphold the one-China policy, Wang said, while China threw its support behind further meetings between Trump and North Korean leader Kim Jong Un.
President Trump and the other leaders of the Group of 20 agreed Saturday to a joint statement that included support for trade reforms, which was a chief USA objective for the summit.
Many major business leaders in both the United States and China had hoped for some sort of truce or partial deal in what is seen as an escalating trade dispute between the world's two largest economies.