"We are totally prepared for the second option, not a preferred option," Mr Trump said, referring to military force.
"But if we take that option, it will be devastating, I can tell you that, devastating for North Korea. That's called the military option. If we have to take it, we will."
Meanwhile, a US official said satellite imagery had detected a small number of North Korean military aircraft moving to the North's east coast.
North Korea has been working to develop nuclear-tipped missiles capable of hitting the US mainland, which Mr Trump has said he will never allow.
Marine Corps General Joseph Dunford, chairman of the US Joint Chiefs of Staff, said on Tuesday Pyongyang would have a nuclear-capable intercontinental ballistic missile "soon" and it was only a matter of a "very short time".
"We clearly have postured our forces to respond in the event of a provocation or a conflict," the general said, adding that the United States has taken "all proper measures to protect our allies" including South Korean and Japan.
"It would be an incredibly provocative thing for them to conduct a nuclear test in the Pacific as they have suggested, and I think the North Korean people would have to realise how serious that would be, not only for the United States but for the international community," Dunford said.
The United States has imposed sanctions on 26 people as part of its non-proliferation designations for North Korea and nine banks, including some with ties to China.
The sanctions target people in North Korea and some North Korean nationals in China, Russia, Libya and Dubai, according to a list posted on the agency's website.
South Korean President Moon Jae-in urged Kim Jong Un to resume military talks and reunions of families split by the 1950-53 Korean War to ease tension.
"Like I've said multiple times before, if North Korea stops its reckless choices, the table for talks and negotiations always remains open," Moon said.
'No winners'
The missive came just hours after South Korea -- whose densely-populated capital Seoul is just 35 miles from the demilitarized zone dividing the Korean peninsula -- asked its US ally to take the heat out of the situation.
Foreign Minister Kang Kyung-Wha visited Washington to warn it was imperative to "prevent further escalation of tensions or any kind of accidental military clashes which can quickly go out of control."
Similarly, China, the North's neighbor and only major ally, warned Tuesday that any conflict would have "no winners."
Foreign ministry spokesman Lu Kang said rhetorical sparring "will only increase the risk of confrontation and reduce the room for policy maneuver."
US Defense Secretary Jim Mattis, visiting India, stressed that Washington wants a diplomatic solution to the North Korean nuclear crisis.
US chairman of the joint chiefs of staff General Joe Dunford said tensions were political rather than military.
"While the political space is clearly very charged right now, we haven't seen a change in the posture of North Korean forces. We watch that very carefully," he said.
Trump and North Korean leader Kim Jong-Un traded barbs in the wake of the North's sixth nuclear bomb and multiple missile tests.
Pyongyang says it needs the weapons to defend itself against the threat of a US invasion.
Firing missives
Alarm over Pyongyang's nuclear and ballistic missile programs dominated the gathering of world leaders at the United Nations, amid fears the heated rhetoric could accidentally trigger a war.
In his UN address last week, Trump delivered the blunt threat to "totally destroy" North Korea if provoked, deriding leader Kim Jong-Un as "Rocket Man".
Kim hit back with a personal attack of his own, branding Trump "mentally deranged" and a "dotard" and warning he would "pay dearly".
The North's Foreign Minister Ri Yong-Ho on Monday called a press conference to hit back at a US bomber mission near the North's coastline and a slew of bombastic warnings from the American president.
Taking umbrage at Trump's weekend tweet that North Korea's leadership "won't be around much longer" if it keeps up its threats, Ri told reporters the international community hoped that a "war of words" would "not turn into real actions."
"However, last weekend, Trump claimed our leadership would not be around much longer," said Ri, who attended this year's UN General Assembly session. "He declared a war on our country."
The White House said Ri's interpretation of Trump's saber-rattling as "absurd".
Fears of a clash were sharpened after US bombers flew off the coast of North Korea on Saturday -- going further north of the demilitarized zone than any US aircraft has flown this century.
"Since the United States declared war on our country, we will have every right to take counter-measures including the right to shoot down US strategic bombers even when they are not yet inside the airspace border of our country," Ri said.
"The question of who won't be around much longer will be answered then."
A Pentagon spokesman stressed the bombers flew in international airspace and had every right to do so.
South Korean intelligence said that, while Pyongyang did not appear to have picked up the presence of the US warplanes over the weekend, it had since bolstered its coastal defenses.
"North Korea relocated its warplanes and strengthened defenses along the east coast," said Lee Cheol-Woo, the chief of the National Assembly's intelligence committee.
