The White House on Monday said Trump and South Korean President Moon Jae-in agreed to use "all means at their disposal" to maximize pressure on North Korea, Xinhua news agency reported.
Trump and Moon underscored the grave threat that North Korea latest provocation poses to the entire world, said the White House in a statement.
"They also pledged to strengthen joint military capabilities," said the statement, adding that Trump gave his in-principle approval to South Korea's initiative to lift restrictions on their missile payload capabilities.
Trump also provided his conceptual approval for the purchase of billions of dollars' worth of military weapons and equipment from the US by South Korea, the statement added.
In a related development, Trump and German Chancellor Angela Merkel discussed the Korean Peninsula nuclear issue in a phone call and both reaffirmed the importance of "close coordination at the UN".
A White House statement said both leaders condemned "continued reckless and dangerous behaviour" by North Korea and Trump noted that the "latest provocation only serves to increase the international community's resolve to counter" North Korea's nuclear program.
The statement also said that all options to address North Korea nuclear issue are on the table.
Meanwhile, China's permanent representative to the UN Liu Jieyi on Monday condemned the latest nuclear test by North Korea and urged the country to return to the track of dialogue. China will not allow chaos and war on the Korean Peninsula, he said.
North Korea on Sunday detonated a hydrogen bomb that can be carried by an intercontinental ballistic missile, North Korea's Central Television announced.
North Korea's nuclear testing and launches using ballistic missile technology violate UN Security Council resolutions.