SEOUL — President Moon Jae-in of South Korea warned on Wednesday that North Korea would face stiffer sanctions if it resumed weapons tests, while crediting President Trump with helping force the North to resume dialogue and strike a broader agreement to improve Korean ties.

“I am giving a lot of credit to President Trump,’’ Moon said at a nationally televised news conference a day after the two Koreas forged their agreement during border talks. “I am expressing my gratitude.’’

President Trump threw his weight behind the Olympics-inspired diplomatic opening by telling South Korea’s leader Wednesday that the United States was open to talks with Kim Jong Un’s government under the right circumstances.

A White House statement said Trump and Moon still agreed on the importance of continuing the ‘‘maximum pressure’’ campaign against North Korea over its development of nuclear weapons — the US-led barrage of international sanctions that is starting to bite the North’s meager economy.

But South Korea’s presidential office also said Trump told Moon to let North Korea understand that there will be no military action of any kind while the two Koreas continue to hold dialogue, the Yonhap news agency reported. On Tuesday, the two Koreas held their first talks in two years and agreed on the North’s participation in the Winter Olympics being held in the South next month.

Speaking later Wednesday, Trump claimed his administration’s pressure campaign had prompted the North Koreans to negotiate with the South, and recounted Moon as telling him the initial meeting was ‘‘extremely good.’’ He voiced cautious hopes for diplomatic success that would benefit not just the United States but the wider world. He played down fears of war.

‘‘We have certainly problems with North Korea,’’ Trump said at a news conference. ‘‘A lot of good talks are going on right now. A lot of good energy. I see a lot of good energy. I like it very much what I’m seeing . . . hopefully a lot of good things are going to work out.’’

Moon has been supportive of the pressure campaign but has long advocated engagement with Pyongyang. He told reporters in Seoul Wednesday that he’s open to meeting with Kim to resolve the North Korean nuclear standoff, although he said the success of such a summit must be guaranteed before the meeting can be realized.

Trump has previously scoffed at the futility of talking with the North, but when the inter-Korean dialogue was proposed last week he claimed credit and declared in a tweet, ‘‘talks are a good thing.’’ The White House said Moon had briefed Trump on the outcomes of the North-South talks on Tuesday, and ‘‘thanked President Trump for his influential leadership in making the talks possible.’’

North Korea made a surprisingly conciliatory gesture during the talks, promising to send a delegation of athletes, cheerleaders, and journalists to the Winter Olympics being held next month in the South Korean town of Pyeongchang. The North also agreed to more talks with the South, including a dialogue between their militaries, to ease tensions and improve ties.

This week’s talks, in the border village of Panmunjom, were the first governmental dialogue between the Koreas in more than two years, and the agreements they produced were hailed as a welcome reprieve for South Koreans after a year of talk of war over the North’s nuclear and long-range missile programs.

But they also came amid concern that Moon might end up facilitating Kim’s strategy of fracturing the US-led sanctions campaign and driving a wedge between Seoul and Washington.

Addressing such concerns, Moon said there was a limit to how far the two Koreas could go in improving ties if North Korea did not move toward dismantling its nuclear weapons program.

“The two issues — improving inter-Korean relations and resolving the North Korean nuclear issue — cannot be separated,’’ Moon said. “If the North provokes again or does not show sincerity on revising its nuclear problem, the international community will continue to apply even stronger sanctions and pressure.’’

“My government has no intention of easing sanctions unilaterally,’’ he added, dismissing speculation that he might lift some of the sanctions imposed by his conservative predecessors, like the closing of a joint factory park in the North Korean town of Kaesong.

But Moon, a vocal critic of Washington’s plan to use military force to resolve the North’s nuclear threat, reiterated that the ultimate goal of sanctions and pressure must be to force North Korea to negotiate. He emphasized that his top national security and foreign policy goal was to prevent war on the Korean Peninsula.

Material from the Associated Press was used in this report.