It was a message emphasizing not only the pressure to denuclearize that has been focus for the Moon administration's North Korea policy, but also its efforts to improve inter-Korean relations and achieve peace on the peninsula.
On preconditions for reopening talks with North Korea, Tillerson said "we'll know it when we see it".
But Tillerson appeared more conciliatory on Monday.
Last week, Mr Tillerson said North Korea needed to cease both its missile launches and nuclear weapons tests for talks to begin. Kang also said she "felt it was an occasion where North Korea acutely sensed its isolated diplomatic position". He's not specifying what those are.
North Korea has previously used misogynistic slurs to describe former South Korean President Park Geun-hye, the country's first woman leader.
The UN Security Council on Saturday imposed its toughest round of sanctions yet against Pyongyang over its two intercontinental ballistic missile (ICBM) tests in July.
With China steadfastly taking issue with the United States' deployment of the Terminal High Altitude Area Defense missile shield in South Korea, the minister likened Beijing's position to "putting the cart before the horse", indicating without North Korean threats, the system would not be necessary.
ASEAN Foreign Ministers on Saturday released a statement urging North Korea to "immediately comply fully" with the UN Security Council resolutions. The regime threatened "strategic" and "physical" actions against the US, which spearheaded the sanctions.
China and Russian Federation went along, but urged the US and South Korea to scale back joint military exercises and a missile defense program that have raised the ire of North Korea.
Tillerson aide R.C. Hammond said that after a productive first day, Tillerson spent several hours preparing for Day 2. Susan Thornton, acting assistant secretary for the U.S. State Department, had counted on a "general chorus of condemnation" directed at the regime during that gathering.
North Korean Foreign Minister Ri Yong-ho made similar comments during an annual regional security conference in Manila on Monday.
Ri was spotted at the gala smiling and toasting with the other foreign ministers. Aside from calling for more sanctions, Trump's approach has centered on enlisting China - the North's biggest trading partner - and others to lessen ties to Pyongyang. Trump's administration began floating potential plans to punish China for its trade practices in what was widely perceived as a reaction to China's inaction on North Korea.
But Washington says it will be watching closely to ensure that China doesn't ease up on the North - if and when the world's attention is diverted elsewhere.
There was no direct reaction from North Korea to Tillerson's remarks but in a statement after the USA secretary of state made his comments, Pyongyang responded robustly to the new sanctions by saying it was ready to teach the United States a "severe lesson" if it attacked. However, among those who favored the decision was the North Korean ally China.
The US ambassador to the UN, Nikki Haley, expressed satisfaction with the new sanctions, saying it increased pressure on Pyongyang to a new level. But there were no signs the USA would acquiesce to China's call for a quick return to negotiations.
The U.S. also warned it planned to rigorously monitor China's compliance with the new penalties.
China will pay the biggest price from the new United Nations sanctions against North Korea because of its close economic relationship with the country, but will always enforce the resolutions, Chinese Foreign Minister Wang Yi said.
Seoul had recently tested the missile shield successfully amid tests carried out by North Korea. But his top diplomat is also laying out a narrow path for the North to return to negotiations. "Can we get to the point where the North Koreans do not see the necessity of having nuclear weapons?" It is being cheered on by President Donald Trump.