Trump has repeatedly railed against the North as he urges the region to take a united front against the threat posed by the isolated nation, which has sparked global alarm with nuclear and missile tests in recent months.
During his trip to Asia, Trump attempted a symbolic stare-down of Kim this week at the heavily fortified border that separates North and South Korea.
Tillerson said that eventually there would be a day when the US and the North decide it's a good time to have that first conversation that would lead to negotiations.
In a speech to South Korea's Parliament on Wednesday, Mr Trump warned Pyongyang not to underestimate the United States, while offering leader Kim Jong Un a better future if he gives up his nuclear ambitions.
North Korea tested its first missile just 22 days after Trump was inaugurated on January 20.
The two leaders also reaffirmed their joint effort to denuclearize North Korea. "It is a hell that no person deserves", Trump said. Trump has threatened to rain "fire and fury" on North Korea in response to the rogue state's rhetoric.
Several weeks later, North Korea fired three short-range ballistic missiles, not toward Guam, but rather into the Sea of Japan. That month it also test-launched a missile over Japan, sparking concern worldwide.
But, there was no test when Secretary of Defense James Mattis traveled through Asia at end of October, nor a test pegged to Trump's trip there now ... so far.
He called on nations to stop financing and trading with North Korea.
Pyongyang described Trump's trip as "nothing but a business trip by a warmonger to enrich the monopolies of the USA defense industry".
"The weapons you are acquiring are not making you safer, they are putting your regime in grave danger", Trump said about North Korea during an address at South Korea's National Assembly in Seoul.
The Trump administration has said all military options remain on the table when dealing with the North Korean threat, but top USA officials have consistently emphasized the U.S.is pursuing a diplomatically led effort, including additional economic pressure.
However Trump, whose strategy has stressed sanctions and military pressure instead of diplomacy, did not spell out any new approach.
"Ultimately, it'll all work out", Trump added.
"I think we have to be a little patient here for at least a few months to see what more we and others can do, including China", McMaster said.
"I'm sure we've got the gear aboard this airplane to make it happen".
Tran said his country placed great importance on its strategic partnership with South Korea and that the had the highest priority in Vietnam's foreign policies, according to the Cheong Wa Dae official.
But the administration shouldn't be too quick to praise North Korea's restraint.