China reacted relatively calmly on Friday after a series of diplomatic broadsides by the United States, expressing anger over new arms sales by Washington to Taiwan but hoping ties could soon be brought back on track.

U.S. officials have said President Donald Trump is growing increasingly frustrated with China over its inability to restrain North Korea's arms and missile programmes.

This week, the United States imposed sanctions on two Chinese citizens and a shipping company for helping North Korea's weapons programmes, announced a $1.4 billion arms sale for Taiwan, and said it would like sick Chinese dissident Liu Xiaobo to be treated "elsewhere".

It has also placed China on its global list of the worst offenders in human trafficking and forced labour and senior U.S. officials have told Reuters that Washington is considering trade actions against Beijing, including tariffs on steel imports.

Trump met Indian Prime Minister Narendra Modi on Monday at the White House and made a point of noting that the United States, India and Japan would be joining together in naval exercises soon in the Indian Ocean, a point that seemed aimed at China.

It's a long way from the "bromance" that Trump and Chinese President Xi Jinping appeared to have at their first summit in April. Trump had made a grand gesture of his desire for warm ties in the meeting at his Florida residence and subsequently called Xi a "good man".

While China said it was "outraged" at the arms sales for Taiwan, and upset with the North Korea-related sanctions, it did not make specific threats of retaliation. In 2010, Beijing threatened to sanction U.S. firms that sell weapons to Taiwan after Washington announced a much bigger $6.4 billion arms package.

Chinese Foreign Ministry spokesman Lu Kang said he hoped the United States can correct its mistakes and get ties back on track "so as to avoid cooperation in important areas being impacted". He did not elaborate.

Jia Qingguo, dean of the School of International Studies at Peking University and who has advised the government on foreign policy, cautioned against interpreting recent events as indicating a shift in China-U.S. relations, saying it was still too early to tell.

"We had a good first summit and a good beginning but the relationship in the long run is characterised by not just cooperation but also conflict," Jia said.

"Arms sales to Taiwan, the South China Sea and East China Sea, and other problems in the relationship will appear. It's a question of how much the two countries will be able to manage these conflicts, whether they can manage them better than the previous administration."

TIES BACK TO NORMAL

Trump and Xi are expected to meet next week on the sidelines of a G20 summit in the Germany city of Hamburg.

China has long been cautious about Trump, China-based diplomatic sources say, believing he is unpredictable and needs to be handled with care.

"How does the Chinese government view Trump? We're still discovering who he is. He often does things we can't predict. We're not clever enough to predict what he'll do," said Shen Dingli, a professor at Shanghai's elite Fudan University.

Trump upset China even before taking office, taking a call from Taiwan President Tsai Ing-wen, overturning decades of precedent of no high-level official contacts between the United States and an island China considers to be a wayward province.

While China has worked hard to get Trump to understand the importance of Taiwan to the China-U.S. relationship, it has never seriously expected Washington to stop selling it weapons, provision for which is explicitly made in U.S. law.

"The U.S. selling weapons to Taiwan is routine," said Shen. "They're selling much less than before, and that's much better. So I don't think there's anything too terrible about that."

Still, the risks around Taiwan are profound.

China's Defence Ministry, responding to the U.S. weapons sales, said Taiwan was the "most important, most sensitive core issue" between the United States and China.

The arms sale came hot on the heels of a U.S. Senate committee approving a bill calling for the resumption of port visits to Taiwan by the U.S. Navy for the first time since Washington ditched Taipei and established ties with Beijing in 1979.

While China's Defence Ministry registered its opposition to the bill on Thursday, spokesman Wu Qian pointed out that as long as they respect each other's core concerns, the Chinese and U.S. militaries can be an "engine of stability" for the two countries.

Shi Yinhong, who heads the Centre for American Studies at Beijing's Renmin University and has advised the government on diplomacy, said it was important people are realistic about the challenges China and the United States face.

"Perhaps people appraised too highly the Xi-Trump meeting. Although the atmosphere was very good, there were still real problems there," Shi said, referring to the Florida summit.

"Maybe you can say that China-U.S. relations have gone back to being normal," Shi added. "Trump has no patience, and nobody can be surprised that he's pushed certain issues to the fore."