Since the beginning of the year, President Trump has refused to answer questions about whether he had spoken directly to North Korea's Kim Jong Un. At the same time, however, he has repeatedly dropped hints that he might have done so.

“I probably have a very good relationship with Kim Jong Un,” Trump told the Wall Street Journal in January. “I have relationships with people. I think you people are surprised.”

Asked directly if he had spoken to Kim, Trump replied: “I'm not saying I have or haven't. I just don't want to comment.” (Trump later disputed the Journal's account of this conversation).

Later in the year, Trump hosted Japanese Prime Minister Shinzo Abe at his Mar-a-Lago resort in Florida. Trump appeared to respond with “yes” when a reporter asked whether he had spoken directly with Kim. However, Trump later clarified vaguely that while communication had taken place “at the highest levels,” he would “leave it a little bit short of that.”

This week, with the U.S.-North Korea relationship looking especially rocky, there is new reason to doubt that any direct communications have taken place between the two leaders so far. As Trump called off a summit with Kim that had been planned for June 12, South Korean officials said that direct communication was still needed between the two.

“It will be much more effective for them to communicate in a direct way to grasp what the other party has in mind,” an unnamed senior official at South Korea's presidential Blue House told Yonhap News agency after South Korean President Moon Jae-in convened a meeting of his security advisers.

“At a time when the U.S.-North summit has hit a snag, there is a need for direct and open communication channels between them,” the official added.

These comments implied not only that South Korea thought direct communication had not taken place so far, but also that the United States' close diplomatic partner on the North Korean situation thought the lack of direct talks was a problem.

Notably, South Korea's Moon spent hours talking with Kim directly during an inter-Korean summit held at the peninsula's demilitarized zone last month.

The U.S. president's indefinite remarks about talks with his North Korean counterpart have already left some to speculate that the pair may have been in some kind of secret direct communication. On Thursday, Bonnie Glaser, a senior adviser on Asia at the Center for Strategic and International Studies, wrote on Twitter that she was “inclined to believe that [Trump] has” spoken to Kim directly.

However, the president often likes to keep his options open when making public comments about North Korea. “Maybe things will work out, and maybe they won’t,” he tweeted in April, not long after he met with Abe in Florida.

After Trump's remarks at Mar-a-Lago alongside Abe that month, the White House pushed back on the idea that the president had implied he spoke with Kim directly. White House press secretary Sarah Huckabee Sanders released a statement saying that the “president said the administration has had talks at the highest levels and added that they were not with him directly.”

Trump may have been obliquely referring to a secret visit to North Korea that then-CIA Director Mike Pompeo made just over a week before. During that visit, Pompeo met Kim. He returned to North Korea as secretary of state for a second visit in May.

On at least three occasions since then, Trump has refused to say whether he has spoken to Kim. Earlier this week, as South Korea's Moon visited the White House, Trump said, "I don't want to say that," adding that dealing with North Korea has been a "good experience."

In a letter addressed to Kim that was published Thursday, Trump called off the planned June 12 summit in Singapore. However, he also said that “a wonderful dialogue was building up between you and me, and ultimately, it is only that dialogue that matters.” The letter added: “Please do not hesitate to call me or write.”

If Trump has not spoken to Kim, it is not clear what is holding him back. He has spoken repeatedly of his openness to direct communication with the North Korean leader despite the tension between the two countries. Asked in early January if he would be interested in talking on the phone with Kim, Trump replied: “Absolutely I would do that. No problem at all.”

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