Mattis said Trump wanted to be briefed on each of the "many military options" for dealing with the North Korean nuclear threat.
"Our commitment among the allies are ironclad," Mattis said. "Any threat to the United States or its territories, including Guam, or our allies will be met with a massive military response, a response both effective and overwhelming."
Mattis called on North Korean leader Kim Jong Un to "take heed" of the UN Security Council's unanimous position against North Korea's nuclear program and again stressed the US military's position.
"We are not looking to the total annihilation of a country, namely North Korea, but as I said, we have many options to do so," Mattis said.
After speaking with Japanese Prime Minister Shinzo Abe for the second time in two days, Trump reaffirmed the US commitment to defending the US and allies "using the full range of diplomatic, conventional and nuclear capabilities at our disposal," according to a White House readout of the call.
The statements come after North Korea claimed it tested a hydrogen bomb
on Sunday in what is its most powerful nuclear test
Trump warned earlier Sunday that the United States was considering stopping trade with any nation doing business with North Korea as a way of dealing with the nuclear threat from Pyongyang.
If carried out, that option could mean a halt to US trade with China, which has supported economic sanctions on North Korea but remains the key economic partner for the rogue nation.
Total trade between the US and China topped nearly $650 billion last year, including exports of about $170 billion and imports of about $480 billion, the vast majority in goods, according to the Office of the US Trade Representative
. That makes China the United States' largest trading partner in goods.
Sunday morning, Trump condemned North Korea's claimed nuclear test
in a series of tweets, calling Pyongyang's words and actions "hostile and dangerous" and saying "talk of appeasement will not work."
"North Korea has conducted a major Nuclear Test. Their words and actions continue to be very hostile and dangerous to the United States," Trump wrote, adding that Pyongyang "has become a great threat and embarrassment to China, which is trying to help but with little success."
"South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!" the President wrote.
Later Sunday morning, Trump again teased the possibility that the US would attack North Korea.
As he left church, Trump was asked, "Will you attack North Korea?"
Trump answered, "We'll see."
Hours before Mattis' statement outside the White House, Trump tweeted that he would meet with administration officials to discuss North Korea. He said the meeting would include the defense secretary, White House chief of staff John Kelly and other military leaders.
A National Security Council official told CNN that national security adviser H.R. McMaster also would attend the meeting, and Gen. Paul Selva, the vice chairman of the Joint Chiefs of Staff, was seen entering the White House.
State Department spokeswoman Heather Nauert tweeted
Sunday morning that Secretary of State Rex Tillerson, who was also scheduled to attend the White House's North Korea meeting, was making calls to his counterparts, including South Korean Foreign Minister Kang Kyung-wha.
US Ambassador to the United Nations Nikki Haley joined her counterparts from Japan, France, the United Kingdom and South Korea in requesting an emergency UN Security Council
meeting on North Korea Monday at 10 a.m. ET.
At the meeting, the US and its allies are looking to push through a new sanctions package, senior administration officials said.
The US is pressing for passage of a resolution to curtail shipments of oil to North Korea on the rationale that it would put severe pressure on Pyongyang, which gets most of its oil from China, the officials said.
If the Chinese were to halt the shipments, it would hamper North Korea's operations, including farming, they said.
North Korea's latest test
This is North Korea's sixth-ever test of a nuclear weapon and the first since Trump took office.
The test was a "perfect success" and the final step in attaining a "state nuclear force," North Korean news anchor Ri Chun Hee said in a televised announcement Sunday.
The news report claimed the weapon was designed to fit atop an intercontinental ballistic missile. The nuclear test follows two successful tests of the long-range missile in July and a shorter-range one in late August.
In a high-level national security meeting, South Korean President Moon Jae-in called the move a "an absurd strategic mistake" that will lead to the international community further isolating Pyongyang.
Japanese Prime Minister Abe said in a statement released by his office Sunday that North Korea's nuclear and missile development "has entered a new level of threat -- more grave and imminent -- against Japan's national security and seriously undermines the peace and security of the region as well as the international community."
The statement adds "given the fact that North Korea has belligerently conducted ballistic missile launches repeatedly this year, the UN Security Council has strongly condemned these actions. Under such circumstances, this nuclear test, which North Korea conducted today despite these calls, is totally unacceptable."
China, North Korea's only real ally and patron, said its neighbor "disregarded universal opposition of the international community" by conducting the test."
"We strongly urge North Korea side to face up to the firm will of the international community on the denuclearization of the peninsula, abide by relevant resolutions of the UN Security Council, stop taking wrong actions that exacerbate the situation and are not in its own interest, and return to the track of resolving the issue through dialogue," the Chinese Foreign Ministry said in a statement.
'No good options'
Arizona Republican Sen. Jeff Flake said on CNN's "State of the Union" Sunday that he would like a "measured" response from the Oval Office.
"Obviously, you'd like a leader that is measured and sober and consistent," Flake said, adding, "We've got a good team around the President."
Flake echoed the administration's previous statements on the North Korean nuclear threat, saying all options needed to be on the table -- including military ones -- and said there is no clear path forward to resolving Pyongyang's continued nuclear development.
"It becomes cliche to say there are no good options here, but there really aren't," Flake said.
Tennessee Republican Sen. Bob Corker, chairman of the Senate foreign relations committee released a statement saying that he had spoken with President Trump's chief of staff John Kelly and made clear his support for "a comprehensive strategy that not only places an emphasis on deterrence but also empowers our allies and partners in the region, who must do far more to confront this threat."
Texas Democratic Rep. Joaquin Castro said on ABC's "This Week" that he does not think Trump's threat last month to rain "fire and fury" down upon North Korea has helped the situation.
"I don't think that it's been helpful," Castro said. "I don't think that it's helpful to get in to a Twitter shouting match with a 32-year-old dictator, Kim Jong-un, in North Korea. I think, unfortunately, that it's escalated the tension and the situation. And he needs to let his diplomats and his military generals and others handle this situation."
During a meeting at his golf club in New Jersey last month, Trump said
in response to the North Korean leader's threats against the United States that Pyongyang would "be met with fire and fury like the world has never seen."
Meanwhile, Florida Republican Sen. Marco Rubio in a statement called North Korea's actions "a sober reminder that all nations, including China, must do everything in their power to stop and reverse Pyongyang's growing nuclear and missile programs. We cannot live in a world held hostage by Kim Jong Un's nuclear blackmail, and I support U.S.-led international efforts to maximize pressure against the North Korean regime and its foreign enablers."
Experts say it is nearly impossible to verify with certainty North Korea's claim that it detonated a hydrogen bomb, which is also known as a thermonuclear weapon, or whether it can actually be used successfully on a missile. Thermonuclear weapons typically use a fission explosion to create a fusion reaction, which is far more powerful than a fission reaction.
NORSAR, an independent seismic monitor, estimated the blast created a yield of about 120 kilotons. The tremors caused by North Korea's Sunday test were at least 10 times more powerful than the fifth test, Japanese officials said. An official at the Korea Meteorological Administration estimated the blast was about 50 kilotons.
The test came just hours after North Korea released images of Kim inspecting what it said was a hydrogen bomb ready to be put on top of an intercontinental ballistic missile, the type of weapon the country would need to use to deliver a nuclear warhead to far-away locations.
Sunday's test comes almost one year after Pyongyang's fifth nuclear test last September, which triggered a 5.3-magnitude seismological event. That took place on September 9, the country's Foundation Day holiday. North Korea claimed it set off a thermonuclear weapon during that test, but experts said the data showed it was more likely a boosted fission weapon.