Trump has engaged in an escalating war of words with North Korean leader Kim Jong-un, trading insults amid rising tensions between the two countries rivals.
"Presidents and their administrations have been talking to North Korea for 25 years, agreements made and massive amounts of money paid," Trump tweeted.
It "hasn't worked, agreements violated before the ink was dry, makings fools of US negotiators. Sorry, but only one thing will work!"
Trump returned to the theme when he appeared on former governor Mike Huckabee's show on Trinity Broadcasting Network television on Saturday, blaming previous administrations for not having adequately addressed the issue before.
This "should have been handled 25 years ago, it should have been handled 10 years ago, it should have been handled during the Obama administration," the president said, referring to his Democratic predecessor Barack Obama.
The president also told journalists at a recent gathering with military leaders to discuss Iran, North Korea and the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group that the current period "could be the calm before the storm," declining to clarify his remarks.
In recent days, as Secretary of State Rex Tillerson flew home from meeting with top Chinese officials, Trump tweeted that his envoy was "wasting his time" in trying to probe North Korea's willingness to talk.
Insults and threats
The message came after Tillerson had revealed there were backchannels between US and North Korean officials.
James Mattis, the US defence secretary, later expressed support for the diplomatic track in testimony before the Senate Armed Services Committee.
"The defence department supports fully Secretary Tillerson's efforts to find a diplomatic solution, but remains focused on the defence of the United States and our allies," Mattis said.
In his debut speech at the United Nations General Assembly, Trump threatened to "totally destroy" North Korea if it threatens the US or any of its allies, deriding Kim as "Rocket Man" and warning he is on a "suicide mission."
Kim responded by calling Trump a "mentally deranged dotard".
Source: Al Jazeera and news agencies