(CNN) After President Donald Trump stepped into North Korean territory on Sunday and then held his third meeting with Kim Jong Un, he claimed that his predecessor, Barack Obama, had tried and failed to secure a meeting with Kim.

"President Obama wanted to meet, and Chairman Kim would not meet him. The Obama administration was begging for a meeting. They were begging for meetings constantly. And Chairman Kim would not meet with him," Trump said during a news conference with South Korean President Moon Jae-in.

Former senior aides to Obama say this is a lie. Independent experts also say it is entirely baseless.

Facts First: There is no evidence that Obama ever sought a meeting with Kim Jong Un, let alone that he was "begging" for a meeting or seeking a meeting "constantly."

Former Obama officials have vehemently rejected Trump's claim. Ben Rhodes, former deputy national security adviser to Obama, told CNN on Sunday: "There's no mystery here: it's just a lie with no supporting evidence and no basis in anything. It's not even an exaggeration, it's just not true."

Rhodes said Obama "never even considered" seeking a meeting with Kim. Later in the day, Susan Rice, former Obama national security adviser, wrote on Twitter : "At the risk of stating the obvious, this is horse-sh*t."

"This probably comes as no surprise, but there's zero truth to Trump's claim. It's utterly fabricated garbage," said Van Jackson, author of On the Brink: Trump, Kim, and the Threat of Nuclear War, who served as senior country director for Korea at the Department of Defense under Obama. "Obama never even deliberated on whether to meet Kim because circumstances were never appropriate. It was never in the conversation. I don't always agree with Ben Rhodes's judgments, but this is a factual issue and he's right about this."

Asked for comment on Sunday, Katie Hill, Obama's current communications director, responded with a link to a tweet in which Rhodes said Trump was lying.

We can't know everything that occurred behind closed doors during Obama's tenure. But experts on US relations with North Korea who did not serve in the Obama administration also said they were certain that Obama did not seek a meeting with Kim in any way.

"Though the Obama administration sporadically tried to restart negotiations, there was never discussion of a presidential summit. It would have been very much out of keeping with policy. Past administrations would not have considered a presidential summit before a major accomplishment had been made, and more likely at the end of a disarmament process," said Adam Mount, director of the Defense Posture Project at the Federation of American Scientists. "The president (Trump) has invented this idea out of thin air for reasons passing understanding. If he's trying to argue that Kim Jong Un likes him more, I for one can't understand why he would take pride in that."

Sung-Yoon Lee, a professor of Korean studies at Tufts University, said Trump has made multiple false or misleading claims about US-Korea relations. Given this record, Lee said, "I feel reasonably sure there is no one in this world who will credibly confirm that Obama sought a summit with Kim Jong Il or Kim Jong Un while he was in office."

In a debate during the Democratic presidential primary in 2007, Obama famously said "I would" when asked if he would be willing to meet "separately, without precondition," with the leaders of North Korea, Cuba, Iran, Syria and Venezuela. But he did not end up seeking such a meeting with either Kim.

Obama pursued a North Korea policy that came to be known as "strategic patience," a phrase used by then-Secretary of State Hillary Clinton in 2009 . The policy was to largely decline to directly engage with the Kims' regime, let alone at the presidential level, as long as they refused to stop their belligerent behavior.

"President Obama showed no interest in meeting with either Kim Jong Il or Kim Jong Un. Especially after the collapse of the February 2012 'Leap Day Deal' and the nuclear test about a year later, he showed hardly any interest in negotiating with Pyongyang at all," said Joshua Pollack, editor of the Nonproliferation Review and a senior research associate at the Middlebury Institute of International Studies at Monterey. "The entire notion of 'strategic patience' meant ignoring the issue to the extent possible."

From the beginning of the Obama administration, Kim Jong Il insisted on negotiating directly with the US. Obama, however, tried to convince him to return to the six-party talks that included Russia, China, South Korea and Japan. When Obama sent special envoy Stephen Bosworth to Pyongyang in 2009, for example, the goal was to revive the six-party talks

The US and North Korea did agree to the so-called "Leap Day" deal in February 2012, in which North Korea agreed to suspend nuclear testing, long-range missile testing and uranium enrichment in exchange for US food aid. The deal failed within two months, and hopes for the resumption of the six-party talks were dashed.