By Steve Holland and Roberta Rampton

WASHINGTON (Reuters) - U.S. President Donald Trump will discuss how to rein in North Korea's nuclear program with Chinese President Xi Jinping later this week in what a senior White House official said on Tuesday would be a test for the U.S.-Chinese relationship.

Trump and Xi are to meet on Thursday and Friday at Trump's Mar-a-Lago retreat on the Atlantic coast in Palm Beach, Florida. It will be their first face-to-face meeting since Trump took office on Jan. 20, and trade and security issues are to figure prominently in their talks.

"We would like to work on North Korea together," the official said in a briefing for reporters. "This is a test for the relationship."

Trump wants China to do more to exert its economic influence over unpredictable Pyongyang to restrain its nuclear and missile programs, while Beijing has said it does not have that kind of influence.

In an interview with the Financial Times last weekend, Trump held out the possibility of using trade as a lever to secure Chinese cooperation.

In the same interview, Trump was quoted as telling the FT that Washington was ready to address the North Korean threat alone, if need be.

The White House official -- speaking just as North Korea fired a projectile believed by South Korea's military to be a ballistic missile into the sea -- said the situation had become more urgent.

"The clock is very, very quickly running out," the official said. "All options are on the table for us."

Trump does not plan to give in to Chinese pressure for the United States to withdraw its THAAD anti-missile system in South Korea, which Beijing considers destabilizing.

Trump has said he expects the meeting to be a difficult one given his belief that China has taken advantage of U.S. trade policies to help its economy and hurt U.S. job creation.

He plans to discuss with Xi a new "elevated" and streamlined framework for a U.S.-Chinese dialogue with "clear deadlines for achieving results," the senior White House official said.

He will discuss significant trade and economic concerns with Xi in what the official called a "candid and productive manner."

(Reporting by Steve Holland and Roberta Rampton; Editing by Sandra Maler)