Trump's comment came the day after Tillerson disclosed 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.
"We are probing. We have lines of communication with Pyongyang", AFP quoted the USA diplomat as saying.
The remarks came just hours after it was revealed that the USA and North Korea have opened several channels of communication.
Secretary of State Rex Tillerson's public acknowledgment that the USA has direct channels to North Korea has underscored his role as an administration moderate when it comes to reining in the regime over its nuclear weapons.
"We ask, 'Would you like to talk?' We have lines of communications to Pyongyang - we're not in a dark situation, a blackout".
Shi Yongming, an associate research fellow at the China Institute of International Studies, which is affiliated with China's Foreign Ministry, said Mr Tillerson's remarks about direct channels to Pyongyang were "positive news". The US State Department later said that the DPRK has so far refused to negotiate about its nuclear program.
The US was in direct communication with the regime, he said, adding, "we can talk to them, we do talk to them".
While Tillerson has said similarly moderate things before - in August he noted North Korea's "restraint" and said the US wanted more goodwill gestures from the regime - his latest remarks in Beijing appeared tailored for a Chinese audience.
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Great expectations: US Secretary of State Rex Tillerson and China's President Xi Jinping meet the press. "Whether through diplomacy or force is up to the regime @StateDept". At the time, Trump tweeted that, while he appreciated China's efforts, they have "not worked out".
He reiterated that Washington would not recognize North Korea as a nuclear power but also has no plans for regime change. Tillerson blamed North Korea for the rising tensions, saying that if it would stop testing missiles, that "would calm down things a lot".
Asked if the President's tweets indicate he has chose to abandon the diplomatic track on North Korea, a senior administration official told CNN: "We are still committed to a diplomatic approach".
U.S. -North Korean communications are long-standing.
"The whole situation is a bit overheated right now", he said.
North Korean officials have suggested that Trump's threats amount to a declaration of war.
Trump delivered a speech to the United Nations in September in which he referred to the North Korean dictator as "rocket man", an insult he has used several times, including in Sunday's tweets.
"At present it's an impasse, neither the US nor North Korea dares to initiate a war despite fierce rhetoric", Shi said. But he insisted that it was up to the North to halt missile launches.