The Trump administration is attempting a balancing act in its confrontation with North Korea, using bellicose rhetoric and promises of military help to America’s allies to defend against Pyongyang while trying to coax China to apply economic and political pressure on its traditional ally.

Vice President Mike Pence visited the demilitarized zone dividing the Korean Peninsula Monday, and stressed President Donald Trump’s willingness to use military force to resolve crises. He declared an end to the Obama administration’s foreign...