At no time, officials said, was there any indication that a nuclear attack had been launched on the United States.

The Federal Communications Commission announced Saturday afternoon it had begun “a full investigation into the FALSE missile alert in Hawaii.”

The alert went out at about 8:10 a.m., lighting up phones of people still in bed, having coffee by the beach at a Waikiki resort, or up for an early surf. “BALLISTIC MISSILE THREAT INBOUND TO HAWAII. SEEK IMMEDIATE SHELTER. THIS IS NOT A DRILL,” it read.

Hawaii has been on high emotional alert — it began staging monthly air-raid drills, complete with sirens, in December — since President Trump and Kim Jong-un, the leader of North Korea, began exchanging nuclear threats. It would take about 37 minutes for a missile launched from North Korea to reach Hawaii, taking a path of about 5,700 miles.

Within moments of the alert, people flocked to shelters, crowding highways in scenes of terror and helplessness. “I was running through all the scenarios in my head, but there was nowhere to go, nowhere to pull over to,” said Mike Staskow, a retired military captain.

Ray Gerst was vacationing on Oahu with his wife to celebrate their 28th wedding anniversary. Just as they pulled up for their tour of Kualoa Ranch, they received the alert.

“All the buses stopped, and people came running out of the ranch and said, ‘Just sit still for a minute, nobody get off the bus, nobody get off the bus,’” he said.

They were taken into the mountains, Mr. Gerst said, and dropped off at a concrete bunker. They sheltered in place for about 15 minutes, he said, during which time they had no cell signal.

“It was scary,” Mr. Gerst said. “I mean, there was no intel.”

At Konawaena High School on the Island of Hawaii, where a high school wrestling championship was taking place, school officials, more accustomed to responding to alerts of high surf or tsunamis, moved people to the center of the gym as they tried to figure out how to take shelter from a missile.

“Everyone cooperated,” said Kellye Krug, the athletic director at the school. “Once they were gathered, we let them use cellphones to reach loved ones. There were a couple kids who were emotional, the coaches were right there to console kids. After the retraction was issued, we gave kids time to reach out again.”

Matt LoPresti, a state representative, told CNN that he and his family headed for a bathroom. “I was sitting in the bathtub with my children, saying our prayers,” he said.

In Washington, Lindsay Walters, a deputy press secretary, said that President Trump had been informed of the events. “The president has been briefed on the state of Hawaii’s emergency management exercise,” she said. “This was purely a state exercise.”

“What happened today is totally inexcusable,” Senator Brian Schatz of Hawaii said. “The whole state was terrified. There needs to be tough and quick accountability and a fixed process.”

The false alert was a stark reminder of what happens when the old realities of the nuclear age collide with the speed — and the potential for error — inherent in the internet age.

The alert came at one of the worst possible moments: when tension with North Korea has been at one of the highest points in decades, and when the government of Kim Jong-un, North Korea’s leader, has promised more missile tests and threatened the possibility of an atmospheric nuclear test. But the cellphone alerting system was in the hands of state authorities; the detection of missile launches is the responsibility of the United States Strategic Command and Northern Command. It was the military — not Hawaiian officials — who were the first to come out and declare that there was no evidence of a missile launch.

During the Cold War there were many false alarms. William J. Perry, the defense secretary during the Clinton administration, recalled in his memoir “My Journey at the Nuclear Brink” a moment in 1979 when, as an undersecretary of defense, he was awakened by a watch officer who reported that his computer system was showing 200 intercontinental ballistic missiles headed to the United States. “For one heart-stopping second I thought my worst nuclear nightmare had come true,” Mr. Perry wrote.

It turned out that a training tape had been mistakenly inserted in an early-warning system computer. No one woke up the president. But Mr. Perry went on to speculate what might have happened if such a warning had come “during the Cuban Missile Crisis or a Mideast war?”

The United States faces an especially difficult problem today, not just because of tense relations with North Korea but also because of growing fears inside the military about the cyber vulnerability of both the nuclear warning system and nuclear control systems.

Because of its location, Hawaii — more than any other part of the United States — has been threatened by escalating tensions and the risks of war. Preparations had already begun, including an air-raid siren alert on Dec. 1, the start of what officials said would be monthly drills.

On Friday, the day before the erroneous alert, several hundred people attended an event in Honolulu sponsored by the Chamber of Commerce in which military commanders, politicians and others discussed the threat to the islands’ population.

“The U.S. is the designated recipient — and that’s because we are public enemy No. 1 to North Korea,” Dan Leak, a retired Air Force lieutenant general and Pacific Command deputy commander, was quoted as saying in the Honolulu Star Advertiser.

In a keynote speech to the group, Admiral Harry B. Harris Jr., commander of the United States Pacific Command, was quoted as saying: “While the possibility of a nuclear strike is slim, we now live in a world where we must be prepared for every contingency.”

The Hawaii Emergency Management Agency has been holding “are you ready” drills. As a chain of islands, Hawaii is subject to all kinds of threats — hurricanes, volcanoes, earthquakes and tsunamis — but officials have made clear that none is more urgent now than the threat of an attack by North Korea, given how little time there would be between an alert and the detonation of a bomb.

The fifth page of an emergency preparation pamphlet issued by the Hawaii Emergency Management Agency features a picture of a rocket lifting off. “Nuclear Threat — Unlikely But Cannot Ignore It.”

Mr. Rapoza, the agency spokesman, said that the shift-change drill was intended to make sure that incoming staff members were up to date with computer operations.

Mr. Rapoza said he did not know if anyone would be disciplined for the mistake. “At this point, our major concern is make sure we do what we need to do to reassure the public,” he said. “This is not a time for pointing fingers.”

The panic the followed the alert — if relatively short-lived — gripped the island. There were reports of cars seeking shelter by parking inside a highway tunnel that cuts through a mountain. People in Hawaii tend to know what to do to protect themselves to threats of a tsunami or a hurricane. The prospect of nuclear annihilation was entirely new terrain.

“So this was the most terrifying few minutes of my LIFE!” Paul Wilson, a professor at Brigham Young University in Hawaii, said on Twitter. “I just want to know why it took 38 minutes to announce it was a mistake?!?”

Chris Tacker, a veteran who lives in Kealakekua, said the mistake had left her angry and frustrated.

“I didn’t know where to go,” she said. “Anyone try to dig a hole in lava? Good luck trying to build a shelter. I’m stocking my liquor cabinet.”

Still, she added, “If we don’t have our sense of humor about this, it’s all over.”