Asked at an off-camera briefing at the Pentagon if there are military options that would not put Seoul at "grave risk?"
Alarmed by North Korea's advancing weapons programs, many conservatives in South Korea have called for the reintroduction of US tactical nuclear weapons in the South.
However, none made any direct reference to Trump's belligerent message to the United Nations meeting.
However, Moon has taken a tougher stance against the neighbor to the north since Pyongyang's recent provocations.
"And the bottom line is that, when the missiles - were they to be a threat, whether it be to USA territory, Guam, obviously Japan's territory - that would elicit a different response from us". "The bottom line is that, when the missiles - were they to be a threat, whether it be to USA territory, Guam, obviously Japan - Japan's territory, that would elicit a different response from us", he said.More news: West Ham United 3-0 Bolton Wanderers
North Korea "must immediately cease making reckless choices that could lead to its own isolation and downfall and choose the path of dialogue", Moon said.
Mr Trump and his Chinese counterpart Xi Jinping discussed "North Korea's continued defiance of the worldwide community and its efforts to destabilize Northeast Asia" by phone, the White House said.
The United Nations Security Council on September 11 unanimously approved a new resolution, banning Pyongyang's textile exports and capping its oil imports.
September has seen a significant ratcheting up of already sky-high tensions with North Korea.
Defense Secretary James Mattis said Monday that the USA has not moved to shoot down any of North Korea's test missiles because "those missiles are not directly threatening any of us". "What we've done with the sanctions is we are putting the leader in North Korea in a position to be aware that the global community, voting unanimously twice now in the United Nations Security Council, seeing the increasing diplomatic isolation that comes with it, comes with the economic sanction that there's a penalty to be paid for ignoring worldwide concerns and norms".More news: LCEC, FPL report on power outages
Mattis said that the USA has military options available to counter North Korea that wouldn't necessarily create a grave risk of retaliation against Seoul.
F-15K fighter jets fly over Korea along with U.S. B-1B bombers and F-35B stealth fighters in a joint drill on Monday.
China's official news agency, Xinhua, said that during the phone conversation "Xi also expressed sympathy and solicitude to Trump and the American people for the hurricane attacks on the United States over the past few days".
South Korean President Moon Jae-in and his Czech counterpart, Milos Zeman, agreed Tuesday to strengthen their countries' strategic partnership while also expanding their cooperation to new areas, including bio, artificial intelligence and information, and communications technology.More news: Wilkins: Chelsea should bring back Costa