"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man,"
Trump wrote on Twitter, using his nickname for North Korean leader Kim Jong-un. "Save your energy Rex, we'll do what has to be done!"
Trump has threatened to "totally destroy" North Korea in the wake of its nuclear and ballistic missile tests, stoking fears of an armed clash on the Korean Peninsula.
In an apparent bid to ease the tensions, Tillerson said Saturday that the US maintains channels of communication with Pyongyang and is not in a "dark situation, a blackout."
"We can talk to them. We do talk to them," he told reporters in Beijing.
The State Department added in a statement that North Korea has yet to show an interest in discussing its denuclearization.
North Korea has posed the biggest security challenge to the US, with Joint Chiefs of Staff Chairman Gen. Joe Dunford saying last week that it is only a matter of a "very short time" before the regime develops a nuclear-tipped ballistic missile capable of reaching the mainland US.
Pyongyang has refused to back down despite increasing sanctions on the regime, saying the weapons programs are a deterrent against US hostility.
"Being nice to Rocket Man hasn't worked in 25 years, why would it work now?" Trump added in a tweet sent later in the day.
"Clinton failed, Bush failed, and Obama failed. I won't fail."
The president was apparently referring to past agreements that sought to dismantle Pyongyang's weapons program in exchange for economic aid. The North Korean regime reneged on those deals by carrying out new nuclear and missile tests.
Many experts say North Korea could stage another provocation this month to coincide with key anniversaries, including the founding anniversary of the ruling Workers' Party of Korea on Oct. 10.
The regime conducted its sixth and most powerful nuclear test on Sept. 3 after launching two intercontinental ballistic missiles in July.
"DPRK will not obtain a nuclear capability. Whether through diplomacy or force is up to the regime," State Department spokeswoman Heather Nauert said on Twitter, using the acronym of North Korea's official name, the Democratic People's Republic of Korea.
"Diplomatic channels are open for Kim Jong-un for now. They won't be open forever." (Yonhap)