(Adds Yang's comments, paragraphs 7-8, 12)

WASHINGTON, Feb 8 (Reuters) - U.S. Secretary of State Rex Tillerson and China's top diplomat Yang Jiechi reaffirmed their countries' commitment to exert pressure in Pyongyang over its nuclear weapons on Thursday, the U.S. State Department said.

Yang was on a two-day visit to Washington that began on Thursday. His talks were also expected to cover the sensitive U.S.-China economic relationship after recent tit-for-tat actions that have raised fears of a trade war between the world's two largest economies.

"Both sides reaffirmed President Trump's and President Xi's commitment to keep up pressure on North Korea's illegal weapons and nuclear programs," State Department Spokeswoman Heather Nauert told a news briefing.

Nauert said Tillerson and Yang "agreed on the importance of continuing a constructive and productive relationship aimed at cooperation on mutual challenges and addressing our differences forthrightly."

"They discussed the need to achieve a fair and reciprocal bilateral economic relationship and shared approaches to stemming the flow of deadly narcotics," Nauert said, adding that the two looked forward to continuing discussions at an annual diplomatic and security dialogue in the first half of 2018.

Yang said at the start of his meeting with Tillerson that he would seek to "push forward our very important relationship."

He said in a statement released by China's Foreign Ministry trade and business relations between the two countries were mutually beneficial.

Both sides should open up each other's markets and handle differences appropriately, Yang said.

Beijing and Washington share concerns about North Korea's development of nuclear missiles capable of hitting the United States.

China has backed successive rounds of U.N. sanctions on North Korea but has been wary of U.S. efforts to toughen these further and has been accused by U.S. officials of not fully implementing existing U.N. steps.

"We expect, we hope that China will do more, because we know they can do more in terms of adhering to U.N. Security Council resolutions," Nauert said.

Yang said the international community should support the improvement in relations between North and South Korea, which has come as South Korea hosts the Winter Olympics that will be formally opened on Friday.

The latest trade data showed China's massive goods surplus with the United States narrowed last month, but not to the extent necessary to appease Washington.

"Our president has made very clear our concerns about trade imbalances," Nauert said.