"We have no desire to inflict harm on the long-suffering North Korean people, who are distinct from the hostile regime in Pyongyang," they wrote.
"We are replacing the failed policy of 'strategic patience'... with a new policy of strategic accountability," they added.
North Korean military figures are putting the final touches on a plan to fire four missiles into the waters around the US territory of Guam, to be presented to leader Kim Jong Un by "mid-August." It's not clear if and when Kim will order the launch.
A notice put out by Guam's Joint Information Center on Saturday warned residents how to prepare "for an imminent missile threat."
In the opinion piece, Mattis and Tillerson said North faces a choice: "Take a new path toward peace, prosperity and international acceptance, or continue further down the dead alley of belligerence, poverty and isolation.
Speaking at a meeting of his senior advisers Monday, South Korean President Moon Jae-in echoed the call for Pyongyang to make the "correct choice."
Mattis and Tillerson urged China to take a leading role in bringing Pyongyang to the negotiating table. "The region and world need and expect China to do more," they wrote.
Later Monday, China announced a full import ban on North Korean mineral resources and seafood would be effective Tuesday.
They're part of the tougher sanctions approved by the United Nations Security Council
earlier this month following two intercontinental ballistic missile tests by North Korea in July.
South Korea: Missile development not yet complete
During a televised briefing, Moon's defense minister, Song Young-moo, told Parliament that North Korea's nuclear weapons development program had not reached its final stage.
He said neither the US nor South Korea believe that North Korea has completely gained reentry technology, and there were questions over whether it has succeeded in miniaturizing a nuclear warhead. Both steps would be required before North Korea could launch a nuclear attack.
Song said South Korea can't pinpoint when both could be achieved, but said "it will take at least one to two more years."
Last week, several US intelligence analysts told CNN they believe North Korea "probably" possesses a miniaturized nuclear warhead
The report, originally in the Washington Post
, was the catalyst for Trump's "fire and fury
" rhetoric, which threatened retaliation on Pyongyang should they not cease making threats against the US.
Top military official arrives in South Korea
Gen. Joseph Dunford, chairman of the US Joint Chiefs of Staff, arrived at Osan Air Base
on Monday, meeting South Korean counterpart Gen. Lee Sun-jin.
A Defense Department statement said his visit aims to "reassure allies and improve military-to-military ties during a complicated time in the region."
Lee said the US general had told him that the US "preparing for possible options in case diplomatic and economic measures fail" in the standoff with Pyongyang.
He also said that Dunford had said that he would bring pressure to bear on China to act on North Korea during the Chinese leg of his trip.
Dunford's trip has been long scheduled and was not arranged in response to the North Korean nuclear threat. Dunford will visit also visit key ally Japan, as well as regional superpower China.
US President Donald Trump is due to speak with Japanese Prime Minister Shinzo Abe in a phone call Monday night in the US.
Threat against Guam
The threat to fire four missiles within 25 miles of Guam came last week and led to an escalation of threats between North Korea and Trump.
On Friday, Trump doubled down on his statement that he would unleash "fire and fury like the world has never seen" if Pyongyang continued its threats, saying in a tweet that "military solutions" were "locked and loaded" for use against North Korea.
Chinese President Xi Jinping
and other world leaders have called for calm as both Pyongyang and Washington upped their saber-rattling rhetoric.
Over the weekend, Japan redeployed batteries of its land-based Patriot Advanced Capability-3 (PAC-3) missile interceptors to some of the prefectures over which the North Korean missiles would potentially fly: Shimane, Hiroshima and Koch.
A spokesman for SDF said the missiles were being deployed not to intercept missiles, but rather "just in case." He did not elaborate.
Sim Tack, a senior analyst for private intelligence firm Stratfor, said the Japanese batteries are designed for protecting the area where they are deployed, "(they are) not meant to shoot missiles out of the sky as they pass over Japan at high altitude."
The SDF spokesman added that the country's Aegis ballistic missile defense system was deployed in the waters between Japan and the Korean Peninsula, but would not give a specific location.
'Business as usual'
In a press briefing, Guam Gov. Eddie Baza Calvo and Homeland Security Adviser George Charfauros sought to reassure residents and visitors that Guam remained completely safe.
Calvo said that it was "business as usual" on the island. Charfauros added that the chance of a missile getting through the "various layers of defense" between North Korea and Guam were 0.0001%.
It remains to be seen whether Trump will pick up where he left off Friday and pile more verbal pressure on North Korea.
Either way, tensions seem set to rise as the US and South Korea prepare to hold annual exercises, called Ulchi-Freedom Guardian, which are scheduled to run from August 21-31.
South Korea confirmed the drill would go ahead as planned and the exercises would not be scaled down.
New commentary published by North Korean state media KCNA said "no matter what rhetoric they let out about 'annual, regular and defensive drills,' they cannot cover up the danger of a war outbreak."
The drills have long antagonized North Korea, and China has called for joint exercise to be called off as a concession to North Korea to freeze its weapons program.