US officials said Pyongyang has not responded to communication from the American military about the soldier, Private Travis T King.
North Korea's state media, which in the past reported on the detention of US nationals, have also not commented on the incident so far.
Speaking in Japan, US special envoy for North Korea Sung Kim said the US was "working very hard" to determine King's status and well-being and was actively engaged in ensuring his safety and return.
Kim did not provide any details.
Earlier, State Department spokesman Matthew Miller told a briefing the Pentagon had "reached out" to counterparts in North Korea's Korean People's Army about King.
"My understanding is that those communications have not yet been answered," he said.
The incident comes at a time of heightened tension on the Korean peninsula.
The North has been pressing on with ballistic missile tests, the latest timed for the arrival in the South of a US nuclear-armed ballistic missile submarine for the first time since the 1980s.
Last week, the North launched its newest solid-fuel intercontinental ballistic missile which it said had the longest flight time ever, a test that experts described as a "remarkable" success.
King, 23, was on a civilian tour of the Panmunjom truce village on Tuesday when he suddenly dashed across the Military Demarcation Line that has separated the two Koreas since the Korean War ended in 1953 with an armistice.
King had been fined for assault while stationed in South Korea and served detention before he was escorted to the airport on Monday to board an American Airlines flight to Dallas, Texas, according to a media report and an airport official.
Once past security checks and at the departure gate, he told airline staff he had lost his passport and returned to the terminal, the airport official told Reuters on the condition of anonymity because he was not authorised to speak to the media.
On Tuesday, King was with a group of about 40 on a full-day tour of the Joint Security Area (JSA) operated by South Korean company HanaTour ITC.
In chaotic scenes, King made a dash between the iconic blue buildings that straddle the border and ran over the line, a witness who was on the same tour said.
"Someone ran close to me very fast and I thought, 'What is going on?'," Sarah Leslie from New Zealand told Reuters.
"I don't think anyone who was sane would want to go to North Korea, so I assumed it was some kind of stunt."
The US government appeared to make little headway in determining the fate of the soldier.
State Department spokesman Miller said Sweden has been engaged as it acts as a diplomatic channel for Washington which remains technically at war with North Korea.
"We are still trying to gather information here about the whereabouts of Private King," he said.
"The administration has and will continue to actively work to ensure his safety and return him home to his family."
White House spokeswoman Karine Jean-Pierre told a briefing the Biden administration was still gathering the facts.
South Korea's defence ministry said it was communicating with the United Nations Command that oversees the JSA but did not comment further.
