MILES O'BRIEN: The U.S. and its Asian allies are trading barbs in the wake of North Korea's latest missile test early today.

Nick Schifrin has our report.

NICK SCHIFRIN: It was an alarming way to wake up, 6:00 a.m. on Japan's Hokkaido Island, and the air raid sirens go off as a North Korean missile flies unseen above.

Residents posted videos on social media, and received a text that was also displayed on computer screens: "Please take refuge in a sturdy building or underground." Never mind most Japanese homes don't have a basement.

WOMAN (through interpreter): They said please get into a solid building, but we were thinking ours here would be gone in the first blast.

NICK SCHIFRIN: The test shook a key U.S. ally, admitted Japanese Prime Minister Shinzo Abe.

SHINZO ABE, Prime Minister, Japan (through interpreter): The North Korean missile, which passed over our nation, represents the greatest and gravest threat to our nation ever. It also is an egregious threat to the peace and stability of the Asia Pacific region.

NICK SCHIFRIN: South Korea's response was even more aggressive. The Defense Ministry released video of every step of a drill it called a direct strike on North Korea's leadership: a fleet of American-made F-15s flying two sorties and dropping GPS-guided bombs.

The South Koreans said they hit their mock target. And if that message wasn't direct enough, air force Colonel Lee Kuk-No made it obvious.

COL. LEE KUK-NO, South Korean Air Force (through interpreter): If North Korea threatens the security of the South Korean people and the South Korea-U.S. alliance with their nuclear weapons and missiles, our air forces will exterminate the leadership of North Korea.

NICK SCHIFRIN: The response was so grave because today was unprecedented. The missile, which launched from a Pyongyang suburb, was the first time a ballistic missile designed for a nuclear tip overflew Japan.

It flew for 14 minutes and splashed down 1,700 miles away, almost enough distance to have reached U.S. territory Guam, which the North Koreans previously threatened to target. The North Koreans have now launched more missiles in the last three years than in the last three decades. They say they're responding to U.S.-South Korea exercises that have been ongoing for the last nine days.

The U.S. calls those exercises defensive and computer simulations, as seen in the 2013 version.

But, in Geneva today, North Korea's U.N. ambassador depicted those exercises as preparations for war.

HAN TAE SONG, North Korean Ambassador to the U.N.: It is an undeniable fact that the U.S. is driving the situation of Korean Peninsula towards extreme level of explosion by deploying huge strategic assets around the peninsula to conduct a series of nuclear war drills and maintaining nuclear threats and blackmail for over a half-century.

NICK SCHIFRIN: The aggressive rhetoric drew a curt reply from President Trump that ended, "All options are on the table."

Analysts describe that today's missile test was designed to create considerable chaos, but not confrontation, and it was also designed to create distance between the U.S. and its allies.

CHRISTOPHER HILL, Former U.S. Ambassador to South Korea: They're trying to show that the U.S. is not in a position to do anything for the Japanese right now. And I think it's part of a broader strategy really to kind of try to show the United States is a kind of paper tiger in the region.

NICK SCHIFRIN: Chris Hill was the U.S. ambassador to South Korea and headed the U.S. delegation in talks designed to dismantle North Korea's nuclear program. He advocates a strategy combing diplomacy with sabotaging North Korea's missiles.

CHRISTOPHER HILL: We do need to look at more direct measures in that narrowing space between peace and war. I don't see how we can simply rely on China or rely on some kind of sanctions program.

NICK SCHIFRIN: Just last week, both President Trump and Secretary Tillerson praised North Korea's self-control.

REX TILLERSON, Secretary of State: I am pleased to see that the regime in Pyongyang has certainly demonstrated some level of restraint that we have not seen in the past.

NICK SCHIFRIN: Since then, North Korea launched two sets of missiles. But Ambassador Hill says the U.S. is right to continue talking diplomacy; it just needs to push its point more.

CHRISTOPHER HILL: Diplomacy is a little like the advertising business. If you haven't said it 50 times, you haven't said it at all.

NICK SCHIFRIN: Today's launch shook the region. The U.S. is trying to reassure allies and deter North Korea, which doesn't seem to feel pressure right now to stop its testing.

For the "PBS NewsHour," I'm Nick Schifrin.