President Donald Trump, asked about his message to North Korea after the latest missile test, told reporters: "You'll soon find out", but did not elaborate on what the USA response would be.
Tensions between the U.S. and North Korea have escalated since Trump vowed he wouldn't let the hermit state develop a nuclear weapon capable of reaching America.
North Korea, technically still at war with the South, regularly threatens to destroy the United States, Japan and South Korea and has said before it will pursue its nuclear and missile programmes to counter perceived USA aggression.
"The only time he should meet with him is to get the details of how North Korea will abandon their nuclear weapons program", McCain told reporters.
A US-China confrontation loomed on the horizon as the Chinese defence ministry announced it would hold live-fire drills and test new weapons to counter an anti-missile system deployed next door in South Korea by the United States.
Trump, asked about his message to North Korea after the latest missile test, told reporters: "You'll soon find out", but did not elaborate on what the US response would be.
Still, Pyongyang said Monday it planned to increase its nuclear tests "to the maximum".
The joint drills have just ended, but naval exercises are continuing in the Sea of Japan (East Sea) with a U.S. strike group led by the aircraft carrier USS Carl Vinson. Kim has never met with a foreign leader since taking charge after his father's death in 2011 and hasn't left his isolated country.
Aadhaar mandatory to avoid fake PAN cards: Govt tells SC
The Centre pushed for mandatory Aadhaar cards, saying that it was a more robust and foolproof method than PAN cards, which can be faked.
White House national security adviser Lt. Gen. H.R. McMaster told his South Korean counterpart that the USA would continue to bear the cost of the system, according to a statement Sunday from the office of the South Korean president.
The dispatch of the Carl Vinson was a "reckless action of the war maniacs aimed at an extremely risky nuclear war", the Rodong Sinmun, the official newspaper of North Korea's ruling Workers' Party, said in a commentary on Saturday.
In July previous year, Washington and Seoul agreed to the battery deployment in the wake of missile tests by North Korea, deemed to be threatening by the West.
The US administration advisor added: "And so it's important, I think, for all of us to confront this regime".
The United States has more than 28,000 service members stationed in South Korea.
In 2009, former President Bill Clinton traveled to North Korea to assist in securing the release of two American journalists imprisoned in the country. Prior to that, McMaster had spoken by phone earlier in the day with his South Korean counterpart Kim Kwan-jin, reaffirming that the US, would pay for the THAAD battery under the existing SOFA agreement.
Seoul regularly warns that Pyongyang can carry out a test whenever it decides to do so. "He's dealing with obviously very tough people", Trump said.