U.S. President Donald Trump on Sunday dismissed the prospect of talks with North Korea as a waste of time a day after his own secretary of state said the United States was maintaining open lines of communication with North Korean leader Kim Jong Un.

"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 sarcastic nickname for Kim and seeming to contradict the top U.S. diplomat.

Trump, who has traded insults and threats with Kim in recent weeks amid escalating tensions over Pyongyang’s nuclear and missile programs, later tweeted that his White House predecessors, Bill Clinton, George W. Bush and Barack Obama, had all "failed" on North Korea by "Being nice to Rocket Man,”

“So why would it work now?" he asked.

Kim succeeded his father, Kim Jong Il, as North Korean leader in 2011, during Obama's administration. Previous presidents negotiated with Pyongyang but ultimately failed to prevent it from pressing ahead with its internationally condemned weapons programs.

Tillerson disclosed on Saturday that the United States was directly communicating with North Korea on its nuclear and missile programs but that Pyongyang had shown no interest in dialogue.

"Save your energy Rex, we'll do what has to be done!" Trump said.

Tillerson said during a trip to China that the United States had multiple direct channels of communication with Pyongyang, the first such disclosure from the Trump administration, and that it was probing North Korea to see whether it was interested in dialogue.

Tillerson expressed hope for reducing tensions with North Korea, which is fast advancing toward its goal of developing a nuclear-tipped missile capable of hitting the U.S. mainland.

"We are probing, so stay tuned," Tillerson told a small group of reporters. "We ask: 'Would you like to talk?'" He said the United States had "a couple of, three channels open to Pyongyang."

AIDES DOWNPLAY COMMUNICATIONS CHANNELS

A senior Trump administration official, asked for clarification about Trump's Sunday morning tweets, played down the significance of the communication channels.

"At a time when North Korea is continuing its provocations, the president does not think now is the time to negotiate with them," the official said, speaking on condition of anonymity.

The official also said that to the extent that diplomatic channels exist between Washington and Pyongyang, they are aimed at securing the return of Americans detained by North Korea.

R.C. Hammond, an adviser to Tillerson, denied that his boss had been undercut by Trump’s tweets and rejected any suggestion that the secretary of state should resign.

"Let's resign the idea of resignation. The President just made it clear to the Kim regime the diplomatic offer on the table is cooling," Hammond said on Twitter.

He also downplayed any contacts.

"Channels have been open for months. They've been unused and cooling for months," Hammond wrote.

State Department spokeswoman Heather Nauert made a similar point on Sunday. "Diplomatic channels are open for #KimJongUn for now. They won't be open forever," she wrote on Twitter.

U.S. Representative Adam Schiff, the top Democrat on the House of Representatives Intelligence Committee, wrote on Twitter: "If Tillerson is wasting his time, it’s only because his boss fails to understand the catastrophic consequences of war on Korean Peninsula."

Trump's rhetoric on North Korea has run the gamut, from personal attacks on Kim to veiled military threats, from a denial of any interest in talks to an insistence that he would prefer a diplomatic solution.

After announcing new U.S. sanctions on North Korea last month, he acknowledged diplomacy was still possible, asking: "Why not?". But he has also frequently declared that he had military options at its disposal, although U.S. officials and outside experts have long said a U.S. strike on North Korea would risk massive casualties.