The abandonment of the summit reduces Trump administration hopes of soon reaching a peaceful agreement for Pyongyang to give up its nuclear and missile programs. It leaves U.S. allies and lawmakers scrambling to determine how best to proceed, and discern how Trump wants to treat talks moving forward. U.S. stock markets fell after the president canceled the summit .

"I have spoken to South Korea and Japan and they are not only ready should foolish or reckless acts be taken by North Korea, but they are willing to shoulder much of the cost of any financial burden — any of the costs associated by the United States in operations, if such an unfortunate situation is forced upon us," he said during an event at which he signed a bill rolling back bank regulations .

The president, throwing aside his conciliatory rhetoric, called the meeting's cancellation a "great setback for the world." Touting a "greatly enhanced" American military and the power of U.S. allies, Trump warned Kim against taking "foolish or reckless" action.

President Donald Trump said Thursday that the U.S. military stands "ready if necessary" following his cancellation of a planned summit with North Korea's Kim Jong Un , ramping up already tense rhetoric exchanged between Washington and Pyongyang.

It marked only the latest sudden twist in a dramatic series of interactions between Washington and Pyongyang. Trump's rhetoric Thursday moved closer to the more aggressive stance he took last year, when he threatened to bring "fire and fury" on North Korea and "Little Rocket Man" Kim.

Still, the president said Thursday that he has hopes for a peaceful resolution or even scheduling another summit with Kim in the future as the U.S. puts economic pressure on Pyongyang. He said "nobody should be anxious" and "we have to get this right."

"If and when Kim Jong Un chooses to engage in constructive dialogue and actions, I am waiting. In the meantime, our very strong sanctions, by far the strongest sanctions ever imposed, and maximum pressure campaign will continue as it has been continuing," Trump said.

The Trump administration is considering putting new sanctions on North Korea as early as next week, The Wall Street Journal reported later Thursday.

Trump said he had spoken to Defense Secretary James Mattis about military readiness. Chief Pentagon spokesperson Dana White told reporters that the Trump administration will keep up the economic pressure campaign, and added that "we are ready to fight tonight, that has always been the case." White said, "the way forward is in the hands of the North Koreans."

In a letter to Kim released Thursday, Trump accused the communist dictatorship of "tremendous anger and open hostility" ahead of the meeting. The summit, previously set for June 12 in Singapore, would have marked the first face-to-face meeting between a sitting U.S. president and a North Korean leader.

Trump wrote that canceling the meeting — during which he planned to press for denuclearization — was "for the good of both parties, but to the detriment of the world." In scrapping the historic summit, he again used some of the fiery rhetoric against North Korea he has recently avoided.

"You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used," the president wrote.

Speaking to reporters Thursday, he said dialogue with Kim "was good until recently." He added that "I think I know why that happened," without giving any more details. Trump has previously suggested China may have intervened in the process.

The latest escalation between Washington and Pyongyang came this week, when Vice President Mike Pence warned that the North Korean regime may end up like former Libyan leader Moammar Gadhafi. His government was toppled years after he agreed to give up his budding nuclear weapons program.

Choe Son Hui, a North Korean official, responded by calling Pence's remarks "ignorant and stupid."

After Trump canceled the summit, both American allies and U.S. lawmakers questioned how Trump would proceed with peace talks. A representative for South Korean President Moon Jae-in, who helped to spark diplomatic talks, said his government was "trying to figure out what President Trump's intention is and the exact meaning of it," the country's Yonhap News Agency reported.

On Capitol Hill, Republicans applauded Trump's move and said they felt Kim had dubious intentions entering the talks about potentially abandoning his nuclear and weapons programs. Democrats worried about whether Trump had a plan to proceed in the peace talks.

Asked if he thinks Thursday's developments increase the chance of war, Trump said, "we'll see what happens. I hope that we'll continue onward."

"I think they want to do what's right," he said of the North Korean regime.

— CNBC's Amanda Macias contributed to this report.