"I think even China is beginning to recognize that this presents a threat to even China's interests," Tillerson said during an interview on CBS' "Face the Nation" program
Sunday. He was asked about how North Korea was discussed during last week's summit between US President Donald Trump and Chinese President Xi Jinping.
"President Xi clearly understands, and I think agrees, that the situation has intensified and has reached a certain level of threat that action has to be taken," Tillerson said.
Despite Tillerson's assessment, China hasn't signaled any change in its approach to Pyongyang in the wake of the landmark summit.
China's Ministry of Foreign Affairs didn't mention North Korea in two statements it released after the two leaders met, and on Monday ministry spokeswoman Hua Chunying stuck to Beijing's usual script.
"China's position on the Korean Peninsula issue has been consistent," she said.
"During the China-US presidential summit at Mar-a-Lago, both sides said they were committed to the goal of denuclearizing the peninsula, would continue to comprehensively carry out UN Security Council resolutions related to North Korea, and agreed to keep close communication and coordination on the issue."
Earlier this year, China called on both North Korea and the US to ease tensions on the Korean Peninsula
-- Pyongyang by suspending its nuclear weapon and missile program and Washington by stopping military exercises with South Korea that antagonize Pyongyang.
Hua reiterated this approach at Monday's briefing.
South Korea and China also agreed to take measures against North Korea if the country were to carry out another nuclear test or launch an intercontinental ballistic missile.
"Both sides agreed that despite the international community's warning if North Korea makes strategic provocations such as a nuclear test or an ICBM launch, there should be strong additional measures in accordance with UN Security Council resolutions," said Kim Hong-kyun, South Korea's special representative for Korean Peninsula peace and security affairs.
Warship heads to Korean Peninsula, not Australia
The comments from Washington's top diplomat came as the Pentagon announced it was sending an aircraft carrier strike group to the waters off the Korean Peninsula.
The move of the USS Carl Vinson strike group is in response to recent North Korean provocations, a US defense official confirmed to CNN.
The Vinson and its escorts, including the guided-missile destroyers USS Wayne E. Meyer and USS Michael Murphy and the guided-missile cruiser USS Lake Champlain, left Singapore Saturday and headed toward South Korea rather than planned port calls in Australia, according to a statement from US Pacific Command.
South Korea said the movement of the Vinson strike group "is a result of recognizing the grave situation on the Korean Peninsula."
"Given that many political events are taking place (in April) there is a possibility for a strategic provocation from North Korea such as a nuclear test and missile launch," South Korean Defense Ministry spokesman Moon Sang-kyun said.
Japan, which has seen previous North Korean missile tests fall within 200 miles of its coast, praised the US carrier movement.
"While the regional security environment becomes increasingly difficult to maintain, it's important to secure the power of US deterrence," Chief Cabinet Secretary Yoshihide Suga said.
The carrier strike group's movement comes just days before North Korea celebrates the April 15 birthday of deceased leader Kim Il Sung, the grandfather of current leader Kim Jong Un. There has been much speculation that Pyongyang will test missiles or possibly a nuclear device to mark the day.
The US carrier group also left Singapore just days after North Korea's most recent missile test.
On April 5, North Korea launched a projectile,
later identified as a Scud extended-range missile, into the sea off the Korean Peninsula. There were conflicting accounts about how far it flew. The regime also has recently conducted several missile engine tests as it works to improve its ballistic missile technology.
In September, North Korea says it successfully tested a nuclear warhead.
Pyongyang claims it is pursuing nuclear weapons to defend itself from what it calls US aggression.
Analysts said the movement of the US warships was likely defensive in nature.
Bruce Bennett, senior defense analyst at the Rand Corp. think tank, said in an email to CNN that the US destroyers and cruiser sailing with the carrier are equipped with the Aegis anti-missile system.
"If North Korea were to test some number of ballistic missiles by firing them into the East Sea/Sea of Japan, these warships would have the potential of intercepting the North Korean test missile," Bennett said.
He said they aren't carrying the weaponry needed for a strike against Pyongyang's nuclear program, something analysts consider highly unlikely.
"Because North Korea places most of its assets underground, it will be difficult for the Vinson group to do a lot of damage to North Korea on its own," he said.