Mr Tillerson's latest remarks came just after the United States announced new North Korea-related sanctions targeting Chinese and Russian firms and individuals for supporting Pyongyang's weapons programs.
A Chinese diplomat called the new sanctions a "mistake", according to news reports from Beijing.
JAPAN, the USA and South Korea brushed aside North Korean warnings of "merciless retaliation" yesterday to press ahead with their provocative war games on the Korean peninsula.
Tuesday's sanctions targeted companies and individuals involved in North Korean weapons programs, its coal and oil trade, and its foreign worker program, which the State Department says are three major sources of funding for the North's illicit weapons programs.
Trump has repeatedly said that China, the only major go-between with the North Korean regime, needs to exert more pressure on Pyongyang.
Defense Secretary James Mattis told reporters earlier this week that whatever the North Koreans may say about it publicly, "they know this is a defensive exercise".
The presence of the three senior officers comes after North Korea test-launched two intercontinental ballistic missiles (ICBMs) last month, and then threatened to fire missiles towards Guam, home to 163,000 people and two key US military bases. A far cry from the "fire" and "anger" promised there are only two weeks by us president Donald Trump if North Korea continues to threaten America with its nuclear ambitions.
Government on right track in J&K: Amit Shah
Bhartiya Janata Party president Amit Shah on Saturday addressed press conference in Bhopal during which he focused on corruption and black money.
North Korea has made rapid progress in its march toward developing a nuclear-tipped ICBM that could target the US mainland.
"We hope that this is the beginning of this signal that we've been looking for - that they are ready to restrain their level of tensions, they're ready to restrain their provocative acts, and that perhaps we are seeing our pathway to sometime in the near future having some dialogue", he added.
The test was North Korea's 12th this year.
China has agreed to support U.N. Security Council sanctions on North Korea. He has eased that rhetoric in recent weeks, however, saying last week that the USA is trying to push North Korea towards talks, even as he underscored that a military strike remains an option.
The United States said Tuesday that talks with North Korea may be possible "in the near future" after Pyongyang reacted to tough new UN sanctions with a level of restraint.
Most Western experts accept that North Korea is close to putting a nuclear warhead on an intercontinental ballistic missile (ICBM) that can reach the continental United States, but this has not been independently verified.
The report says while it is relatively easy to send an ICBM into the void of outer space, it is very hard to bring it down in order to attack the US.
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