We should publicly announce an attack on South Korea or our allies will be met with a nuclear response on all nuclear military installations. Multiple Multiple Multiple bunker busters should be dropped his suspected residences. END OF Problem.
To respond to an all out attack from North Korea using conventional weapons instead of nukes would cause great loss of life in the South. Many of those lives would be American.
I say this, if I was president and some fool dictator like this said his government has authorized merciless nuclear attacks on my country, then his country would cease to exist.