The world's two economic powerhouses, the US and China, are gearing up for another big trade war, and they have already started sparring.

U.S. President Donald Trump said Tuesday that he is in "no rush" to speak with Chinese President Xi Jinping about the issue. His comments came after his press secretary, Karoline Leavitt, had said earlier in the day that the two leaders would "meet soon."

His mixed signals follow recent tit-for-tat moves by both sides.

Trump had imposed an additional 10 percent tariffs on Chinese products on Tuesday. His administration wants China to do more to keep fentanyl from flowing into the US.

The press secretary said: "He is not going to allow China to continue to source and distribute deadly fentanyl into our country. That was the reason for this tariff."

But China quickly hit back. The government said it will impose additional tariffs on US goods starting February 10th.

It targeted items such as coal and liquefied natural gas with an another 15 percent in tariffs.

China said it also plans to beef up export controls on rare metals like tungsten, which are important materials used in high-tech industries.

It also filed a complaint with the World Trade Organization, claiming the US moves violate trade rules.