The border closing appears temporary and is intended to let the Pyongyang government focus on the Dec. 28 funeral, The Wall Street Journal reported.
The report did not indicate whether North Korea closed its border with Russia.
Meanwhile, state television repeatedly showed film clips of senior military leaders pledging unconditional allegiance to Kim Jong Il's youngest son and selected successor, whose leadership skills are untested, The New York Times reported.
If the younger Kim is unable to demonstrate his control, the military may become more and more influential in all aspects of government, the Times said.
But the Pentagon said Wednesday it has detected nothing out of the ordinary from the North's military thus far, calling the events a "peaceful transition" of power, The Hill reported.
"This is an opportunity" for North Korea to "join the family of nations," Pentagon spokesman Capt. John Kirby told the Washington newspaper.
North Korea tightened internal security and put troops on alert as the country's new leader led a solemn procession of mourners to the glass coffin of his father and longtime ruler.
The coffin was surrounded by white chrysanthemums and Kimjongilia, a flower named after the deceased leader.
Kim Jong Il died of a heart attack at age 69 while on a train Saturday, the government said.
Kim Jong Un, believed to be 27, was accompanied by senior party and military officials, images provided by the official Korean Central News Agency indicated.
The news agency said North Koreans would trust and follow the younger Kim "under whatever circumstances."
South Korea's government expressed condolences Tuesday to the North Korean people but said it wouldn't send an official delegation to the funeral.
KCNA said Monday foreign delegations would not be invited.