To protect against a North Korean attack, the United States is on the verge of making a new antimissile system operational in South Korea. Mr. Trump said in the interview that he would seek to have South Korea pay for the system, known as the Terminal High Altitude Area Defense system, or Thaad, putting its cost around $1 billion.

Under its arrangement with Washington, South Korea was to provide land and build a base for the Thaad system, while the United States would pay for it and cover its operational costs.

In South Korea, Mr. Trump’s comment shook the election campaign to choose a successor next month to Park Geun-hye, the ousted president. Ms. Park’s decision to accept the Thaad deployment has been one of the most contentious issues on the trail, and Moon Jae-in, the leading candidate, seized on the remarks and, through a spokesman, called for a halt to the deployment.

“We must consider whether it conforms to the spirit of the alliance,” the spokesman, Youn Kwan-suk, said on Friday, accusing Mr. Trump of “demanding unilaterally and without close bilateral consultations that South Korea pay the cost” of the missile defense system.

Rebuffing Mr. Trump, the South Korean Defense Ministry said on Friday that it had no plans to pay for operating the system.

Mr. Trump also said that because of the United States’ sizable trade deficit with South Korea, he intended to renegotiate or end a trade pact with the country. That free trade agreement, called Korus, went into effect in 2012. It contains a framework for trade in both goods and services, and it covers environmental issues as well.

Like all free trade deals, it is designed to remove barriers to commerce. South Korea is America’s sixth-largest trading partner in goods, with $112.2 billion worth of commerce between the two in 2016, according to the Office of the United States Trade Representative. South Korea has a $10.7 billion trade deficit in services with the United States, but a $27.7 billion trade surplus in goods.