Trade talks between the US and China have ended with little progress in a week that has seen the trade war between the two countries heat up.

A White House statement said two days of talks had covered "how to achieve fairness, balance, and reciprocity in the economic relationship".

However, there was no indication of any major breakthrough.

On Thursday, the US imposed a second wave of tariffs on Chinese goods worth $16bn (£12.4bn).

China immediately imposed retaliatory taxes on the same value of US products.

The US has threatened a third round of tariffs on an additional $200bn of Chinese goods, which could come as soon as next month. If this happens, China has said it will respond with tariffs on a further $60bn of US goods.

The talks between the US and China in Washington were the first face-to-face discussions between the two sides since June.

However, hopes were not high of a breakthrough, with President Trump saying on Monday that he did not "anticipate much" from the meeting.

White House deputy press secretary Lindsay Walters said that talks included "addressing structural issues in China", such as its policies over intellectual property and technology transfers.

Mr Trump has said previously that he wants to stop the "unfair transfers of American technology and intellectual property to China" and protect jobs.

In a brief statement, China's Ministry of Commerce said the Chinese delegation had held "constructive and candid" talks on trade issues.

"Both sides will keep in contact about the future arrangement," it added.

President Trump has long been critical of China, and ordered an investigation into Chinese trade policies in August 2017.

By imposing tariffs on Chinese imports he hopes to make life easier for US companies, whose goods will become cheaper within the US by comparison.

However, many US companies and industry groups have testified to the US Trade Representative's Office that their businesses are being harmed.

Many are worried that Chinese retaliatory tariffs will make their products more expensive and reduce demand, and businesses that rely on Chinese imports face higher costs.

Complaint
The tariffs are part of the president's broader "America First" approach, which has also prompted the US to impose higher import duties on steel and aluminium, including from Mexico, Canada and the European Union. All of those countries have retaliated.

Meantime, China plans to file a fresh complaint against the tariffs at the World Trade Organization (WTO), which adjudicates in global trade disputes.

China's commerce ministry says it "clearly suspected" the US of violating WTO rules.

It filed an initial complaint at the WTO in July as Mr Trump imposed his first round of tariffs.