The slightly more optimistic comments came after both sides ramped up their trade war, with China announcing details of new tariffs against U.S. imports on Monday, following the United States' move last week to target Chinese imports.
The U.S. Trade Representative's office said it planned to hold a public hearing next month on the possibility of imposing duties of up to 25% on a further $300 billion worth of imports from China. Cellphones and laptops would be included in that list but pharmaceuticals would be excluded, the office said.
The prospect that the United States and China were spiralling into a fiercer, more protracted dispute that could derail the global economy has rattled investors and led to a sharp selloff on equities markets in the past week.
But speaking in Russia on Monday, in comments relayed by China's Foreign Ministry on Tuesday, the Chinese government's top diplomat, State Councillor Wang Yi, struck a more upbeat tone, noting the talks had made important and substantive progress, as well as facing problems.
While noting that "buckpassing" and pressure were counterproductive and would only invite retaliation, Wang added that there was still hope to resolve the issue in a friendly way.
"We believe that as long as these negotiations are in line with China's general direction of reform and opening up, in line with China's fundamental need for high-quality development, and in line with the common and long-term interests of the Chinese and American peoples, both countries' negotiating teams have the ability and wisdom to resolve each other's reasonable demands, and in the end reach a mutually beneficial, win-win agreement."
Talks are not a one-way street and should be based on equality, he said.
"When negotiating with any country, China must uphold the sovereignty of the country, safeguard the interests of the people, and safeguard the dignity of the people. These principles and bottom lines we have stuck to in the past, and we still have to today."
Trump, who has embraced protectionism as part of an "America First" agenda, said he would talk to Xi at a G20 summit in late June.
"Maybe something will happen," Trump said in remarks at the White House on Monday. "We're going to be meeting, as you know, at the G20 in Japan and that'll be, I think, probably a very fruitful meeting."
Speaking several hours later at a dinner gathering at the White House, Trump said it should be clear in "three or four weeks" if a U.S. trade delegation's trip to Beijing two weeks ago was successful.
"I have a feeling it's going to be very successful," Trump said.
The Shanghai Composite Index and the blue-chip CSI300 both fell 1 percent at the open on Tuesday, but quickly recovered ground, aided by state-backed buying of equities, according to some analysts. The Shanghai benchmark was down 0.4 at the midday break.
Chinese state media on Tuesday kept up a barrage of nationalistic commentary.
The country's top newspaper, the ruling Communist Party's official People's Daily, said in a commentary that the United States needed to "give it a rest" with the complaints that it was losing out to China in the trade relationship.
China is not to blame of the huge trade deficit the United States runs, and China is a hugely profitable market for U.S. companies, the paper said, in commentary published under the pen name "Zhong Sheng", meaning "voice of China".
"U.S. consumers, farmers, businesses and so on have become the victims of the trade frictions provoked by the United States. They are not victims of China's 'unfair competition.'" - Reuters
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