Former Joint Staff Director Lt. Gen. Curtis "Mike" Scaparrotti will replace Thurman as the top American commander on the Korean peninsula this week.
"It''s clear to me, he's in charge up there. And that's what we've been observing for the better part of the time that he's been the new leader," Thurman said.
Kim took the reins of the country in 2011, shortly after the death of his father and former leader Kim Jong-il.
U.S. military drills in early March sparked the most recent game of military one-upmanship between the United States and North Korea that seemingly brought the region to the brink of war.
The U.S. deployed a ballistic missile defense system to Guam and moved Navy ships, armed with anti-missile weaponry, off the Korean peninsula last month, in response to aggressive movements by the North Korean military.
In response, North Korea has put its long-range artillery and rocket units on full alert and shuttering a military hotline with South Korea.
U.S. forces began flying B-2 and B-52 heavy bombers, which are capable of carrying nuclear weapons, in the skies above South Korea last March.
Days after the bomber flights, Kim reportedly gave his military the green light to launch nuclear strikes against U.S. allies in the Pacific and targets inside the U.S.
In the end, Pyongyang eventually backed off its threats, initiating a "provocation pause" between the two countries and restoring stability to the Asia-Pacific region, the Pentagon said last March.
However, the continued threat of the regime's ongoing nuclear weapons work requires constant surveillance by U.S. and allied forces in the region.
"I think we've got to keep a close watch on them every day. And that's what we try to do on the peninsula," Thurman added during a press conference in South Korea.
But last year's escalation dashed Washington's hopes for a new era in American-North Korean relations, Pacific Command chief Adm. Samuel Locklear said during the same briefing.
"I think there was some optimism that [Kim Jong-un] would be a different type of leader and maybe would recognize the path that North Korea has been on is not good for the North Korean people, nor good for regional stability or global stability," Locklear said.
"That said, I think we have been disappointed in what we saw," the four-star admiral added.