North Korean leader Kim Jong Un and President Trump shake hands at their meeting on Sentosa Island in Singapore on June 12. (Evan Vucci/AP)

After his historic meeting with Kim Jong Un, President Trump assured the American people that his summit would help decrease the nuclear threat posed by North Korea. "Sleep well tonight!” he tweeted.

Americans are divided on their confidence in that statement.

Just over half (51 percent) of Americans said it was likely the summit will help decrease the nuclear threat posed by North Korea, according to a Monmouth poll released Thursday.

While not an overwhelming majority, the fact that at least half of Americans feel confident that things are headed in the right direction with North Korea, a country that has long been considered one of America's biggest adversaries, is a move in the right direction for Trump.

“The event was clearly a good photo op for both leaders, but the top goal from the U.S. perspective was reducing the nuclear threat posed by Kim’s regime. The public is more optimistic than pessimistic that this will be an outcome of these talks, but only just slightly,” said Patrick Murray, director of the independent Monmouth University Polling Institute.

Nearly 4 in 10 Americans, 37 percent, are confident in Trump's ability to handle North Korea. But nearly the same percentage, 36 percent, aren't confident in Trump's ability to handle the Kim regime.

The Washington Post previously reported that Trump and Kim viewed the meeting as a success, though how that was exactly being defined was not quite clear:

Kim, or at least his country’s state-run news agency, said the two leaders had decided to end “extreme hostile relations” and described the beginning of a “step-by-step and simultaneous” process that would eventually lead to peace and “denuclearization of the Korean Peninsula.”

Both sides said Trump had agreed to halt military exercises with South Korea. Additionally, according to Pyongyang, the president offered “security guarantees . . . and [to] lift sanctions” as their dialogue proceeded, to which North Korea would respond with “additional good-will measures.”

Critics of the summit say it will ultimately benefit North Korea the most, and a sizable number of Americans agree: 38 percent said North Korea gained more than the United States from the meeting, and 45 percent said it made Kim look stronger on the world stage. Only 12 percent said the United States gained more. Nearly 40 percent said both gained equally.

The data suggest that while Trump and his surrogates are confident of the summit's success, the American public isn't as sure and still has a lot of questions. But most Americans seem glad it happened: More than 7 in 10 think the summit was a good idea, an increase from 63 percent in April.

Time will tell whether the progress Americans are hoping for will actually manifest. Despite the hopeful pledges, as The Post's Joby Warrick reported Wednesday, North Korea's nuclear warheads — at least 20 to perhaps 60 — remain in bunkers somewhere in the rugged hills north of Pyongyang:

Work continues daily in the country’s radiochemistry lab near Yongbyon, where plutonium for new bombs is extracted from spent fuel rods. Just across a small river from the lab, testing continues on a 20-megawatt reactor capable of producing nuclear fuel for scores of additional bombs.