US President Donald Trump and Chinese President Xi Jinping have expressed optimism about resolving their bitter trade disputes ahead of a high-stakes meeting planned for the two leaders at the end of November in Argentia.

But within hours of the upbeat assessments, the US Justice Department took aim at another Chinese firm it accused of unfair practices, part of an across-the-board pressure campaign by the Trump administration targeting China.

Still, investors cheered the resumption of dialogue and a report that Trump was taking steps to resolve the tariff war, with shares in Asia hitting three-week highs on today and the dollar softening.

Both countries presidents have expressed optimism in resolving their issues. (Getty)

Trump said on Twitter that trade discussions with China were "moving along nicely," and that he planned to meet with Xi on the sidelines of the G20 leaders summit, after the two had a "very good" phone discussion yesterday.

Bloomberg later reported, citing people familiar with the matter, that Trump wants to reach a trade agreement with China at the G20 meeting and that after the call with Xi he had asked officials to begin drafting potential terms.

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.

In comments to state media, Xi said he hoped China and the United States would be able to promote a steady and healthy relationship, and that he was willing to meet with Trump in Argentina.

"The two countries' trade teams should strengthen contact and conduct consultations on issues of concern to both sides, and promote a plan that both can accept to reach a consensus on the China-US trade issue," Xi said on CCTV state television.

Xi was quoted by CCTV as saying after the call with Trump that the two leaders had hoped to expand trade cooperation.

Neither leader specified any details of potential progress in their first known direct discussion in several months.

Trump administration officials have said that trade talks with China cannot resume until Beijing comes up with specific actions it is willing take to meet US demands for sweeping changes to policies on technology transfers, industrial subsidies and market access.

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 $US500 billion-plus ($A690b) exports to the United States if the disputes cannot be resolved.

Jacob Parker, vice president of China operations at the US-China Business Council in Beijing, said there were plenty of challenges that would require significant negotiations in advance of a meeting between Trump and Xi to ensure success.

"What negotiations have lacked to date has been that (presidential) level of engagement. If President Trump makes an agreement with President Xi, there is nobody above them to overturn it," he said.