Mr. Ri’s reference to the declaration of war appeared to refer to Mr. Trump’s assertion in a Twitter message over the weekend that the North Korean leadership may not “be around much longer” if it continues its threats.

Mr. Ri said that the question of “who would be around much longer will be answered” by North Korea.

It is possible that North Korea’s foreign minister wanted to make clear that it, too, could threaten pre-emptive military action, just as the United States has repeatedly suggested in recent months.

But Mr. Trump’s tweet over the weekend appeared to go further, suggesting that mere threats, rather than a military attack, could drive him to wipe out the country. Whether that was one of his characteristic outbursts or a strategic effort to intimidate North Korea was not clear — even to some of his advisers.

“If the goal is to intimidate the North Koreans, it needs to be understood that they are really hard to intimidate,” said Evans J. R. Revere, a Korea expert who is a former deputy assistant secretary of state.

“They’re not used to an American president saying these things,” Mr. Revere said. “They’re also masters at responding when their leader is attacked.”

The escalation of threats came two days after American warplanes flew close to the North’s coast, going farther north of the Demilitarized Zone — the dividing line between North and South — than any other American air mission since the turn of the century. The Air Force advertised the exercise, which involved only American aircraft, as a direct response to North Korea’s accelerated missile launches and a nuclear test two weeks ago.