President Trump meets with South Korean President Moon Jae-in in the Oval Office on April 11. (Evan Vucci/AP)

President Trump on Thursday signaled he remains open to an incremental deal with North Korea that would help further the negotiations over nuclear disarmament, but he emphasized his administration remains focused on “the big deal.”

Ahead of a bilateral meeting with South Korean President Moon Jae-in in the Oval Office, Trump told reporters that there are “various smaller deals that maybe could happen,” and that the two leaders would be discussing potential increases in humanitarian aid, including food assistance, to the North.

But he also emphasized he expects economic sanctions to remain in place until Pyongyang agrees to a deal to eliminate its nuclear weapons.

Asked if he would accept a “smaller deal” that fell short of that goal to keep talks going, Trump responded: “I’d have to see what the deal is. There are various smaller deals that could happen. . . . You could work out step-by-step pieces, but at this moment we’re talking about the big deal. The big deal is we have to get rid of nuclear weapons.”

Trump abruptly ended his talks with Kim during a summit in Hanoi in late February after the two sides failed to make progress, and there have been no working-level meetings since then. Trump declined to say whether he has been in contact with Kim since their summit.

The president said that a third summit “could happen,” but he did not offer a timeline and added that the negotiations are “step-by-step” and “not a fast process.”

“I enjoyed the summits. I enjoyed being with the chairman,” Trump said of Kim. “They’ve been really productive. But this is not going to go fast. . . . If it goes fast, then it’s not the proper deal.”

Moon’s visit to the White House represented an urgent effort to get the talks back on track and convince Trump to support minor sanctions relief that would open the door to small-scale, cross-border economic projects between South Korea and North Korea.

Trump and first lady Melania Trump met Moon and his wife, Kim Jung-sook, at the South Portico, escorting them into the White House for their meetings.

In brief remarks, Moon said the Hanoi summit was “not a source of disappointment,” suggesting that it was part of a longer negotiation process that could lead to a “bigger agreement.” He added that there will be “no daylight” between the United States and South Korean governments, attempting to dampen reports of friction.

Moon invited Trump to visit Seoul “in the near future,” according to a summary of the meeting released by South Korea’s Blue House, but there was no announcement that such a trip was being scheduled.

Trump is tentatively scheduled to make two trips to Japan in the next two months — to Tokyo for a ceremony marking the changing of the emperor in May and the Group of 20 summit in Osaka in June — where he will meet with Prime Minister Shinzo Abe, who has more conservative views on North Korea.

Trump administration officials have said privately that they have not heard back from their North Korean counterparts after sending messages that they remain open to resuming working-level meetings. The talks in Hanoi broke down after the North offered to close parts of its main nuclear processing facility in exchange for sanctions relief, but the United States demanded that the North commit to complete and irreversible denuclearization before any sanctions are lifted.

Some foreign policy analysts questioned the mixed signals from Trump.

“The policy incoherence on North Korea continues,” Suzanne DiMaggio, an Asia analyst at the Carnegie Endowment for International Peace, wrote on Twitter.

“Trump, with Moon Jae-in sitting at his side, says the process w/ Pyongyang needs to be ‘step-by-step,’ ” she wrote. “Why did he spring on Kim in Hanoi a ‘big deal” insisting on denuclearization up front and then walk away when it was rejected?”

At a Senate hearing on Wednesday, Secretary of State Mike Pompeo told lawmakers that he was unable to answer affirmatively whether the two sides had agreed upon a specific definition of denuclearization. Pyongyang has long insisted that the United States remove its nuclear umbrella over South Korea as part of a deal, but U.S. officials have said that is a non-starter.

Trump said his relationship with Kim remains “strong” and noted that the North has maintained a freeze on nuclear and ballistic missile testing since November 2017.

“This is a much different relationship than it was two years ago,” Trump said. He referred to his announcement, in a tweet three weeks ago, that he would rescind new Treasury Department sanctions on Chinese shipping companies accused of helping the North circumvent existing sanctions.

“I didn’t think they were necessary. I think that sanctions right now are at a level that’s a fair level,” the president said. “We could always increase them.”

Trump reiterated his belief that North Korea would flourish economically if it agreed to a deal to abolish its nuclear weapons program. “I think North Korea has potential as great as anything I’ve ever seen,” he said.