"We would like to work on North Korea together. There is an opportunity," the official said during a conference call briefing.

"We've been ... trying pretty much everything to bring about a safe and denuclearized peninsula. So this is some ways a test of the relationship."

The official stressed the urgency of the problem, saying, "The clock is very, very quickly running out.

"We would have loved to see North Korea join the community of nations. They've been given that opportunity over the course of different dialogues and offers over the course of four administrations with some of our best diplomats and statesmen doing the best they could to bring about a resolution," the official said

"The clock has now run out, and all options are on the table for us," he said without elaborating.

Trump is scheduled to hold his first meetings with Xi at his Mar-a-Lago resort in Florida on Thursday and Friday. North Korea will be one of the most important topics for their discussions as Trump is determined to use Chinese influence over the North to rein in the provocative regime in Pyongyang.

On Sunday, Trump said in an interview with the Financial Times that China should help with the North Korea problem by using the "great influence" it has over Pyongyang, warning that if it doesn't, the U.S. will solve the problem on its own, and that won't be good for anyone.

Trump also said he will use trade as an incentive for China to take action on the North.

On Tuesday, Trump said the North is a "humanity problem," and he will talk about the issue with China's Xi.

"North Korea clearly is a matter of urgent interest for the president and the administration as a whole. I think the president has been pretty clear in messaging how important it is for China to coordinate with the U.S. and for China to begin exerting its considerable economic leverage to bring about a peaceful resolution to that problem," the White House official said.

"Certainly, it is going to come up in their discussions.

Somewhere in the order of just shy of 90 percent of North Korea's external trade is with China. Even though we hear sometimes that China's political influence may have diminished, with North Korea, clearly its economic leverage has not. It is considerable and so that will be one of the points of discussion," he said.

The Trump-Xi meetings will also be watched closely as to whether the U.S. stands up to China for bullying South Korea for hosting the U.S. THAAD missile defense system designed to defend better against ever-growing missile threats from North Korea.

The White House official said that the deployment will go ahead as planned.

"We are familiar with China's objections to THAAD. The United States will always act to defend our allies and to defend our homeland against any threat, particularly one of the nature of the North Korean regime with the kinds of terrible weapons that they're developing. There will be no move away from protecting our South Korean allies and the United States," he said.

The official also said that China's retaliation against the South is "disturbing."

"South Korea is a responsible, friendly, economically dynamic democracy that is seeking together with its ally, the United States, to put in place defensive systems. It doesn't make much sense and at some levels even is disturbing to be punishing South Korea for wanting to do that," the official said.

"If THAAD is a problem to other countries in the region, they need to look to North Korea," he said.