The United States has "many" military options against North Korea, including some that don't put Seoul at risk, Defense Secretary Jim Mattis said Monday.

His comments come after U.S. President Donald Trump's administration ramped up pressure on North Korea on Sunday, warning Pyongyang will be "destroyed" if it refuses to end its "reckless" nuclear and ballistic missile drive.

"There are many military options, in concert with our allies, that we will take to defend our allies and our own interests," Mattis told Pentagon reporters.

He did not provide details, but he responded affirmatively when asked if these included options that would not put Seoul at grave risk.

Mattis also confirmed that Washington and Seoul had discussed the option of sending limited-size "tactical" nuclear weapons to South Korea.

North Korea's weapons drive is set to dominate Trump's address to the United Nations General Assembly on Tuesday and his meetings with South Korean and Japanese leaders this week.

Tensions flared when Kim Jong-Un's regime tested what it termed a hydrogen bomb many times more powerful than its previous device.

The North also fired a ballistic missile over Japan and into the Pacific on Friday, responding to fresh new U.N. sanctions with what appeared to be its longest-ever missile flight.

Amid calls for the U.S. and Japan to shoot down such missiles, Mattis said there was no need to do so because they were not a direct threat.

"The bottom line is that in the missiles, were they to be a threat, whether it be the U.S. territory Guam, obviously Japan, Japan's territory, that would elicit a different response from us," he said.

Meanwhile, China's foreign ministry said that threatening action or rhetoric cannot help resolve the situation on the Korean peninsula after U.S. Mattis hinted about the existence of military options on North Korea.

"Developments in the peninsula nuclear issue up to this point prove that, no matter whether it is military threats in words or in action, they cannot promote and advance a resolution," the foreign ministry spokesman, Lu Kang, said.

"To the contrary, it just adds to tensions and makes achieving the goal of denuclearization on the peninsula appear more complicated and difficult to resolve," he added, responding to a question about Mattis' comments at a regular briefing.