Tillerson was briefing reporters Friday after President Donald Trump's two-day summit with Chinese President Xi Jinping at Mar-a-Lago.
Thick with tension, the conversation this week between Stephen K. Bannon, the chief White House strategist, and Jared Kushner, the president's son-in-law and senior adviser, had deteriorated to the point of breakdown.
The U.S and China made tremendous progress in bilateral ties during meetings with his Chinese counterpart Xi Jinping, President Donald Trump said. Trump has accused China of "raping" the United States and argued that it has engaged in trade abuses to gain an advantage over the US.
Trump's position on democratically ruled Taiwan - which China considers a breakaway province - has been an major irritant since he accepted a protocol-breaking phone call from the Taiwanese president after his election victory.
The officials signaled that the trading relationship between the two countries and North Korea's nuclear program were at the top of the agenda during the meetings, which took place here over 24 hours at Trump's Mar-a-Lago estate.
In a brief appearance after their first round of talks, Mr Trump said he and Mr Xi had made "tremendous progress" and that they would be making "additional progress".
The two leaders instead broadly vowed to work more closely to get the North to abandon its nuclear weapons, a vow that Pyongyang has heard many times before.
Xi expressed "an appreciation" to Trump for informing him of the number of missiles that were launched and explaining the rationale behind the strike, said Tillerson.
UN strongly condemns North Korean missile launch after delay
Vice President Mike Pence, on a tour of Asian allies, has said repeatedly an "era of strategic patience" with North Korea is over.
"Some forces are loud-mouthed that the recent USA military attack on Syria is an action of warning us but we are not frightened by it", the report said, adding that the North's "tremendous military muscle with a nuclear force as its pivot" will foil any aggression by the U.S.
If mishandled, disagreements over approaches to North Korea or bilateral trade could destabilize Northeast Asia or tank the global economy.
Tillerson said the two leaders noted the urgency of the threat of North Korea's weapons program.
"The best way to get China to cooperate with North Korea is to be tough on them with trade, which is the No. 1 thing China's government cares about", Senate Democratic Leader Charles Schumer of NY said.
The U.S. airstrikes this week were aimed at a Syrian air base, but nearly certainly got the attention of another adversary - North Korea.
Trump's barnstorming presidential campaign a year ago appeared to set him on course for conflict with China, which he accused of rigging forex markets and cheating at trade to steal American jobs. "When the president fails to label them a currency manipulator, he gives them a green light to steal our jobs and wealth time and time again".
Trump also said he would prefer that the Federal Reserve keep interest rates relatively low. And he left open the possibility of re-nominating Janet Yellen for a second four-year term as Fed chair.
Associated Press writers Josh Boak in Washington and Christopher Bodeen and Gerry Shih in Beijing contributed to the report.