On Sunday, a North Korean Foreign Ministry official was quoted on state-run media as vowing to step up the country's defenses to protect itself from airstrikes like the US carried out against Syria last week.
Observers have interpreted Tillerson's message as a warning to other global troublemakers, such as North Korea.
White House spokesman Sean Spicer said on Friday that the Syrian attack sends a very strong signal not just to Syria but throughout the world.
The US has been pushing China to put pressure on North Korea to stop its nuclear program and missile testing, but Trump said in an interview published Sunday with the Financial Times that the US would be prepared to act alone to stop North Korea.
One option "is to target and kill North Korean leader Kim Jong Un and other senior leaders in charge of the country's missiles and nuclear weapons and decision-making", NBC news reported, quoting multiple top-ranking intelligence and military officials.More news: Jan Vertonghen backs Tottenham flop to prove critics wrong
The North called the airstrikes "absolutely unpardonable" and said they prove its nuclear weapons are justified to protect the country against Washington's "evermore reckless moves for a war".
Last month, USA nuclear envoy Joseph Yun came to Seoul and met with presidential candidates and campaign officials.
"We will bolster up in every way our capability for self-defense to cope with the USA evermore reckless moves for a war and defend ourselves with our own force", KCNA added.
North Korea last week conducted a ballistic missile test in spite of U.N. Security Council resolutions banning such launches.
In appearances on the Sunday news shows, Tillerson said advances in North Korea's ballistic missile program concerned the USA the most.More news: Davis Cup: Djokovic gives Serbia 1-0 lead over Spain
South Korea on Friday lauded the summit agreement between the USA and Chinese leaders to work closely together to convince North Korea to curb its nuclear program.
Rather than continue its tough talk on North Korea, Markey told CNN's "New Day" on Thursday that Trump should ask Xi "to tighten the screws" with economic sanctions.
Earlier this month, Trump suggested the US might take action unilaterally if China wasn't willing to do more. "China will either decide to help us with North Korea or they won't".
A US defense official said Saturday that the strike group will provide a show of presence in the region.
Diplomatically isolated North Korea considers Syria a key ally. North Korea denied involvement in that attack.More news: Daniel Cormier says he is done fighting at 205lbs