Officials held a press conference around 3:45 p.m. ET confirming earlier reports that a man was in fact found dead.
Authorities were visibly emotional and thanked Kim's family for their support during the search.
"They have been true champions throughout this whole ordeal and we just want them to know our thoughts and our prayers have been with them from Day One," said Lt. Gregg Hastings of the Oregon State Patrol. "This obviously is extremely tough on those who have had an emotional commitment throughout the last several days here."
KTVU earlier reported that airborne rescuers spotted a flash in a heavily wooded area and caught a glimpse of a man laying face down. Searchers were being lowered from the helicopter to assist the man.
Fresh search teams had joined the hunt earlier in the day for the San Francisco man who set out on foot Saturday to help his family out of the snowy coastal mountains. Kim had left clothing and other items such as bits of an Oregon map that appeared arranged to guide searchers, officials said Wednesday.
"He is a sharp individual and has a strong will to live," Jackson County Sheriff Mike Winters said. "He has done a heck of a job out there."
The clothing, which was wet, included two gray sweat shirts, a red T-shirt, a sock and a blue girl's skirt, Hastings said. Family members said Kim had taken the items when he left.
"They were laid out in a well defined area, in a pattern," Hastings said. The pattern led officers to believe that "little signs are being left by James."
Searchers also found a pair of gray pants they believed belonged to Kim. The family said he was wearing the pants over blue jeans when he left.
But an expert on hypothermia said it was a bad sign: victims of cold often feel a false sense of warmth and shed their clothes.
Teams were trying to resume their search Wednesday, but were hampered by fog which they hoped would lift by midday.
Searchers planned to drop 18 rescue packages containing clothing, emergency gear and other survival provisions into the area Wednesday in hopes that Kim could find one. The packages, clear plastic bags the size of pillows, also contained a note from his family.
Searchers said the packages would be dropped in a 3-square-mile area where "hot spots" showed up two nights earlier in thermal imaging.
"This is frustrating. We are so close," Josephine County Undersheriff Brian Anderson said. "There are people pouring their heart and soul into this. We are not going to quit until we find him."
Temperatures at night in the search area have been dipping below freezing in lower elevations. No precipitation is expected until Friday.
Kim's wife, Kati, and two daughters were rescued Monday at their car, stuck in the snow on a remote road.
When he left the car Saturday, James Kim went about two miles along the road, and then headed down into a drainage area, said Lt. Gregg Hastings of the Oregon State Police.
About 100 rescue workers and four helicopters were searching for Kim, following his footprints down a drainage called Big Windy Creek that leads to the Rogue River.
Anderson said he does not know why Kim went into the drainage area. "I hope to have the opportunity to ask why he did that," he said.
Kim, a senior editor for the technology media company CNET Networks Inc., had two lighters and was wearing tennis shoes, pants and a heavy coat, but no hat, Anderson said. He would likely be within about five miles of the car, he said.
The Kims had been missing since Nov. 25, when they left Portland and headed home after a holiday trip to the Pacific Northwest.
Kati Kim told officers they were traveling south from Portland on Interstate 5 and missed the turnoff to a state highway, Oregon 42, that leads through the Coast Range to Gold Beach, where they planned to stay at a resort.
Officers said the couple used a map to choose the road they were on. "They got the map out — a regular highway map — that showed the route," Anderson said.
However, it wasn't clear whose map the couple used. The 2005-2007 state highway map distributed by the Oregon Department of Transportation has a warning in red print, inside a red box: "This route closed in winter." A Rand-McNally map did not have a similar warning.
On Monday, searchers in a private helicopter hired by the family spotted Kati Kim, 30, and daughters Penelope, 4, and Sabine, 7 months. They were released from a hospital in Grants Pass on Tuesday.
After leaving Portland on Interstate 5, search leaders said, the couple missed a turnoff that leads to the coast and took a wrong turn on a twisty mountain road they chose as an alternative.
Stuck, they used their car heater until they ran out of gas then burned tires to stay warm and attract attention. With only a few jars of baby food and limited supplies, Kati Kim nursed her children.
The area's complicated road network is commonly used by whitewater rafters on the Rogue River or as a shortcut to the coast in the summer, but it is not plowed in the winter.
<i>The Associated Press contributed to this report.</i>