Tensions have flared since US President Donald Trump, responding to the North's latest missile tests, warned it of "fire and fury like the world has never seen".
The North in turn threatened to test-fire its missiles towards the US Pacific island of Guam.
The war of words has sparked global alarm, with world leaders including Chinese President Xi Jinping urging calm on both sides.
Moon, a left-leaning leader who has previously advocated dialogue with the North, urged it to "stop all provocations and hostile rhetoric immediately, instead of worsening the situation any further".
"Our top priority is the national interest of the Republic of Korea (South Korea) and our national interest lies in peace," Moon told advisers in a meeting.
"We cannot have a war on the Korean peninsula ever again," he said. The 1950-53 conflict cost more than a million lives, left cities in ruins and perpetuated the division of the peninsula.
"I am confident that the US will respond to the current situation in a calm and responsible manner in line with our policy direction," Moon said.
The latest US and North Korean sabre-rattling has sparked concern that a miscalculation by either side could trigger a catastrophic conflict, although many analysts voice doubts over such a prospect.
Any conflict between the North and the US could have devastating consequences for Asia's fourth-largest economy, with Seoul within range of Pyongyang's vast conventional artillery forces.
Also within range are many of the 28,500 US troops stationed in the South.
The tests are seen as a milestone in the North's quest to develop a nuclear-tipped missile capable of hitting the US mainland.
Since then the North and Trump have locked horns in fiery exchanges, with Trump saying on Friday that US troops were "locked and loaded" in case a military solution became necessary.
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