Tillerson's comments at a regional security forum in Manila were the latest U.S. attempt to rein in Pyongyang's nuclear and missile programs after months of tough talk from U.S. President Donald Trump.
The U.N. Security Council on Saturday imposed its toughest round of sanctions yet against Pyongyang over its two intercontinental ballistic missile (ICBM) tests in July.
But Tillerson appeared more conciliatory on Monday.
"When the conditions are right, then we can sit and have a dialogue around the future of North Korea so they feel secure and prosper economically," Tillerson told reporters.
"The best signal that North Korea can give us that they are prepared to talk would be to stop these missile launches," said Tillerson, adding that "other means of communications" were open to Pyongyang.
There was no direct reaction from North Korea to Tillerson's remarks but in a statement after the U.S. 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.
The U.N. Security Council unanimously imposed sanctions on North Korea aimed at pressuring Pyongyang to end its nuclear program. The sanctions could further choke North Korea's struggling economy by slashing its $3 billion annual export revenue by a third.
The United States has remained technically at war with North Korea since the 1950-53 Korean conflict ended in an armistice rather than a peace treaty. The past six decades have been punctuated by periodic rises in antagonism and rhetoric that have always stopped short of a resumption of active hostilities.
The Trump administration's attempts to pressure North Korea into abandoning its nuclear and missile ambitions have so far gained little traction, and Pyongyang has only stepped up its tests, launching two ICBM tests last month.
Tillerson's remarks might be an attempt to try another tack by the United States, which also has tried to get Pyongyang's ally China to use its influence to prevent North Korean leader Kim Jong Un from building a nuclear arsenal.
Tillerson said halting missile test launches, which have worried neighbours South Korea and Japan, was a first step toward dialogue.
He said Washington would not "specify a specific number of days or weeks" before deciding that North Korea had indeed halted its tests.
Joel Wit, director of 38 North, a Washington-based North Korea monitoring project, said he did not think North Korea would agree to a suspension of missile tests unilaterally as a precondition to talks without, for example a suspension of large-scale military exercises held regularly by the United States and South Korea, which it has denounced as a prelude for invasion.
Tillerson said the support of China and Russia for the sanctions sent a strong message to North Korea about what was expected of it.
Chinese Foreign Minister Wang Yi urged "the North Korean side to calmly handle the resolutions". He said in Manila on Sunday that Pyongyang should "not do anything unbeneficial towards the international community such as a nuclear test."
In a statement to the Manila forum on Monday, Pyongyang said it would never place its nuclear program on the negotiating table as long as the United States maintained a hostile policy against the North.
It noted its intercontinental ballistic missile tests last month proved the entire United States was in its firing range.
North Korea says its ICBMs are a legitimate means of defence. It has long accused the United States and South Korea of escalating tensions by conducting military drills.
The Pentagon said on Monday it was reviewing bilateral ballistic missile guidelines with South Korea that could allow Seoul to have more powerful missiles.
Under the current guidelines, last changed in 2012, South Korea can develop missiles up to a range of 800 km (497 miles) with a maximum payload of 500 kg (1,102 pounds).
China's Wang said the core of the Korean Peninsula issue is a security issue, not an economic one, as North Korea believes it faces an external security threat, while other parties believe Pyongyang's nuclear and missiles programs are a threat.
In a phone call, South Korea's Moon and Trump said they would continue cooperating to rein in North Korea, particularly ahead of a regular joint military drill set for late August, South Korean presidential office spokesman Park Su-hyun said.
The White House said the two leaders "affirmed that North Korea poses a grave and growing direct threat" to most countries around the world.
(Additional reporting by Patricia Zengerle, David Shepardson, David Brunnstrom and Matt Spetalnick in Washington, Amy Tennery in Bedminister, N.J., Ben Blanchard in Beijing, and Karen Lema, Neil Jerome Morales and Manolo Serapio Jr in Manila; Writing by Martin Petty and Alistair Bell; Editing by Bill Trott and James Dalgleish)
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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