“The President can instantly start the joint exercises again with South Korea, and Japan, if he so chooses,” Mr. Trump wrote, adding, “If he does, they will be far bigger than ever before.”

The tweets came five days after the president abruptly canceled a trip to Pyongyang by his secretary of state, Mike Pompeo, citing a lack of progress in negotiations for the North to relinquish its nuclear arsenal.

North Korea is pushing the United States to endorse a declaration to end the Korean War, while the White House is demanding that Pyongyang declare a full inventory of its nuclear weapons and missiles — and to set a timetable for dismantling them. Neither side has budged, and the atmosphere among officials below Mr. Trump and Mr. Kim has become increasingly sour.

Mr. Trump has long linked North Korea with China and trade. On Friday, when he called off Mr. Pompeo’s trip, he claimed that the deepening trade fight was leading China to hamper the nuclear talks.

On Wednesday, he said somewhat cryptically, “Donald J. Trump feels strongly that North Korea is under tremendous pressure from China because of our major trade disputes with the Chinese government.”

But administration officials say they do not see a link between North Korea and the trade dispute. Moreover, they say China has largely stuck to its commitments under United Nations sanctions not to trade with North Korea, though there is anecdotal evidence of increased commercial activity along the border between the North and China.

The Chinese Ministry of Foreign Affairs tartly dismissed Mr. Trump’s comments on Thursday. Asked about the remarks, Hua Chunying, a spokeswoman for the ministry, said: “Sorry, we cannot accept, and will not accept, all the fancy buck-passing by the U.S. side.”