In an early morning tweet, Trump said: "Kim Jong Un of North Korea made a very wise and well reasoned decision. The alternative would have been both catastrophic and unacceptable!"
Trump appeared to be referring to Kim's decision to put a hold on launching four missiles
into the waters around the Pacific island of Guam, as North Korea had previously threatened.
North Korean state media reported Tuesday that Kim had reviewed a previously announced plan to fire the missiles on a trajectory over western Japan, but had decided not to go ahead with the proposal for now.
The report came after US Secretary of Defense James Mattis warned that if North Korea fired on US territory it would be "game on."
Speaking at the Pentagon on Monday, Mattis told reporters: "You don't shoot at people in this world unless you want to bear the consequences."
'Fire and fury' provokes response
Tensions between the two countries have been at their highest point in months after Trump made a series of inflammatory comments against the rogue state on August 8.
Trump said he would unleash "fire and fury like the world has never seen"
on North Korea if it continued to threaten the United States.
In response, North Korea announced its plan to fire missiles at Guam, which it said would "send a serious warning signal to the US."
Dubbed the "tip of the spear," Guam is a vital part of the US's military presence in the Pacific
as well as being home to thousands of US servicemen and their families.
North Korea's announcement provoked strong condemnation from not only the US but also Japan, over whose mainland the missiles would have to fly to reach Guam.
Japan deployed missile defense systems to several military bases around the country over the weekend as a precautionary measure.
But on Tuesday, North Korean state media said it would wait to see what the "foolish Yankees" did next
before committing to the launch.
Contentious drills imminent
Trump's praise for Kim's decision comes less than a week before the start of joint military drills between the US and South Korea.
Dubbed the Ulchi-Freedom Guardian, the 10-day annual exercises begin on August 21 and are almost certain to antagonize Pyongyang, which believes they are a rehearsal for an invasion.
The US and South Korea insist the drills are purely defensive.
On Tuesday, China, North Korea's closest diplomatic ally, urged Washington and Pyongyang to "put the brakes" on all provocative actions and statements.
In a call with Russia, Chinese Foreign Minister Wang Yi stressed there was no military solution to tensions on the Korean Peninsula, only a diplomatic one.