TOKYO — For those worried about a nuclear war between North Korea and the United States, the weekend disclosure by Secretary of State Rex W. Tillerson that the two nations were in direct communication was a rare glimmer of hope that a diplomatic resolution to the standoff might be possible.

But President Trump’s remarkable public rebuke of Mr. Tillerson’s efforts — he said the nation’s top diplomat was “wasting his time” — was a sharp reminder of how difficult it will be for the two sides to reach an agreement even if they begin serious talks.

Apart from conflicting messages from President Trump and his aides about their willingness to enter negotiations, the hurdles to a meaningful dialogue with North Korea are high, and it will be even more difficult to reach a deal with the North than it was with Iran, analysts said.

The key difference, of course, is that North Korea has already developed nuclear weapons, even if it has not yet demonstrated that it can hit the United States with one.