But for weeks before the meeting, which started as a Twitter offer by the president for Mr. Kim to drop by at the Demilitarized Zone and “say hello,” a real idea has been taking shape inside the Trump administration that officials hope might create a foundation for a new round of negotiations.

The concept would amount to a nuclear freeze, one that essentially enshrines the status quo, and tacitly accepts the North as a nuclear power, something administration officials have often said they would never stand for.

It falls far short of Mr. Trump’s initial vow 30 months ago to solve the North Korea nuclear problem, but it might provide him with a retort to campaign-season critics who say the North Korean dictator has been playing the American president brilliantly by giving him the visuals he craves while holding back on real concessions.

While the approach could stop that arsenal from growing, it would not, at least in the near future, dismantle any existing weapons, variously estimated at 20 to 60. Nor would it limit the North’s missile capability.