Rex Tillerson said, “We’re not your enemy,” the US wanted a dialogue at some point.
But a Republican senator said President Donald Trump had told him there would be a war with North Korea if its missile programme continued.
Pyongyang claimed its latest missile could hit the US west coast.
The second test of an intercontinental ballistic missile (ICBM) on Friday, celebrated by North Korean leader Kim Jong-un, was the latest to be conducted in defiance of a United Nations ban.
“We do not seek a regime change, we do not seek the collapse of the regime, we do not seek an accelerated reunification of the peninsula, we do not seek an excuse to send our military north of the 38th parallel,” said Mr Tillerson, referring to the border between the Koreas.
“We’re not your enemy, we’re not your threat but you’re presenting an unacceptable threat to us and we have to respond.”