The stakes are high if this summit goes awry, analysts say, particularly if North Korea responds by resuming missile or nuclear testing.
Later in the day, Trump himself tweeted out that there was, indeed, a deal "very much in the making".
The administration is also lacking an ambassador to South Korea as well as a special envoy for North Korea, and there are a slew of questions to address.
No venue or date for the meeting has been determined, but Mr Trump's prompt acceptance set off a flurry of activity.
While an actual in-person meeting between a sitting USA president and North Korea's leader would be a novel development, an agreement between them on denuclearization would not be.
Mr Trump would become the first sitting United States president to meet with a leader of the reclusive country.More news: US House speaker urges Donald Trump to drop new tariffs plan
Faso said expectations about the Trump-Kim meeting need to be kept realistic.
The South Korean leader might offer to reopen the Kaesong industrial center, which was closed after a North Korean nuclear test in 2016.
"(We) agreed that we will not repeat our past mistakes and continue putting maximum pressure to realise the abandonment (of Pyongyang's) nuclear and missile programme".
Mr Trump agreed to meet Mr Kim by the end of May and the two Koreas will hold a summit by the end of next month. The envisioned meeting would be a historic first between leaders of the two Cold War foes.
Later, at a political rally in Pennsylvania, when Trump mentioned Kim's name, the crowd booed.
It comes after Kim has referred to Trump as a "senile dotard" and Trump has repeatedly referred to the North Korean leader as "Little Rocket Man".More news: Victor of $560M Powerball jackpot can stay anonymous, U.S. state judge rules
Sanders also denied that the Thursday announcement had been haphazard in any way or that key foreign policy officials had been left out. "We've not heard anything directly back from North Korea, although we expect to hear something directly from them".
Mike Chinoy, CNN's former senior Asia correspondent and author of "Meltdown: The Inside Story of the North Korean Nuclear Crisis", said "an asterisk" would hover above the talks until North Korea officially confirms its buy-in.
The officials say Trump told Netanyahu that until now the three European powers only proposed "cosmetic changes" that he doesn't find satisfactory. "But at the end of the day, the ultimate person to lead that negotiation or that conversation and be at the table will be the president". In 1994, President Bill Clinton agreed to provide North Korea with $4 billion in energy aid in exchange for...wait for it...denuclearization.
Pompeo went on to make clear that the administration is not going to start playing nice with Kim just because of the dictator's new promises that he wants to denuclearize and stop developing new ways to launch nukes at the United States and its allies.More news: Broadcom's proposed Qualcomm bid blocked on security grounds
- Budget session of Parliament: Stalemate on Day 6, protests continue
- 'Chilling': Virat Kohli shares picture of wife Anushka Sharma kissing him
- Oregon Ducks to open NCAA women's tournament against Seattle
- Bollywood Singer Aditya Narayan Arrested For Rash Driving
- Federer wins, Djokovic out at Indian Wells
- Apple Maps Now Shows Bike Sharing Stations in Montreal, Toronto and Beyond
- WOMEN'S NCAA: UConn, Irish, Louisville, Miss St top seeds
- After Ivan Rakitic, Philippe Coutinho supports Neymar's Barcelona return from PSG
- John Cena Challenges The Undertaker to a Match at WrestleMania
- ''Bookkeeper of Auschwitz'' Oskar Groening dies before starting sentence