Trump, during a meeting with Chinese vice premier Liu He in the Oval Office, floated the idea of following up on a potential trade deal with China with a second phase deal that addressed the issue of military spending and arms production.
Australian shares are expected to open slightly lower as global investors await the outcome of the latest US-China talks, aimed at ending their protracted trade dispute.
Markets have been rattled by the uncertainty around the negotiations.
Washington wants sweeping changes to China's economic and trade policies, while Beijing wants Trump to lift expensive sanctions on Chinese goods.
Goods trade between the United States and China totaled $660 billion a year ago, according to U.S. Census Bureau data, consisting of imports of $540 billion from China and $120 billion in exports to China. The two sides had appeared to make some progress on the issue in January, when China approved a handful of GMO crops for import.
"Trump is pressing China at the last stage of the talks, requiring it to offer greater concessions on market opening and strengthen the supervision over the implementation of promises", said Li Yishuang, a Shanghai-based economist at China Securities Finance Co. who specializes in worldwide trade.
Analysts say any agreement is likely to include banner announcements that China has agreed to increase purchases of American commodities like soybeans and fuel.
The talks are due to continue for a third day on Friday.
On February 22, Trump said he planned to meet with Xi "in the not-too-distant future".
Trump boasts about the money the government collects in tariff payments, though he often insists incorrectly that foreigners pay the tab rather than Americans. A person familiar with the text said China so far agreed only to contemplate not to retaliate if the USA took action against Beijing, but stopped short of a formal pledge to refrain from counter-punches.
Trump said Thursday that any summit would be "here", but he did not specify whether he meant Washington or elsewhere in the United States.
Mr. Trump said he may still close the border if no other steps work, but his focus on tariffs as a more immediate option was striking. The United States wants China to accelerate its approval process and make it more similar to Washington's. Last month, Trump said the tariffs would stay in place for "a substantial period", although whether this would apply to both tranches of goods subjected to the new duties was unclear.
One of the final issues is what will happen to the tariffs the two sides have imposed on about US$360 billion of each other's goods in the past nine months.
Markets have been wobbly throughout the week as investors wait for the USA government's jobs report on Friday and prepare for a new round of corporate earnings reports next week.
Meanwhile, a study revealed that the burden of U.S tariffs on Chinese imports is hurting the American economy contrary to what Trump is claiming.