Brunson made the remarks Wednesday at a forum hosted by the Gold Institute for International Strategy in Washington.
Brunson, who also heads the UNC and the South Korea-U.S. Combined Forces Command, said that, from the UNC's perspective, South Korea begins at the southern fence line of the DMZ.
The 1953 armistice established the DMZ as a roughly 4-kilometer-wide buffer zone, extending about 2 kilometers on either side of the Military Demarcation Line (MDL).
Under Article 3 of South Korea's Constitution, the country's territory encompasses the entire Korean Peninsula and its adjacent islands, including the North, although Seoul does not exercise control over North Korean territory.
The controversy comes amid an ongoing disagreement over who should authorize civilian access to the DMZ.
Ruling party lawmakers have pushed legislation that would give the South Korean government greater authority over access for nonmilitary purposes, while the UNC has maintained that its existing authority is grounded in the Armistice Agreement.
"The UNC has no authority to determine the territorial sovereignty of the Republic of Korea," said Rep. Kim Byung-joo, a ruling Democratic Party lawmaker and presidential special adviser on defense policy, in a Facebook post Saturday.
The defense ministry said Sunday that Brunson's comments reflected his personal views and reaffirmed its firm position on South Korea's territorial sovereignty.
The ministry added that it would continue working closely with the UNC to ensure that South Korea's exercise of sovereignty within the DMZ and the command's armistice responsibilities could coexist.
The UNC also sought to ease the controversy, saying South Korea's sovereignty was beyond question.
It explained that Brunson had been referring to the military and administrative responsibilities assigned to the UNC commander within the DMZ and the Joint Security Area (JSA) under the Armistice Agreement, rather than questioning South Korean sovereignty.
The dispute also follows growing friction between Seoul and Brunson over the planned transfer of wartime operational control (OPCON) from the United States to South Korea.
At the same Washington forum, Brunson argued that changing security conditions, including North Korea's missile advances, required updated military standards for the transfer.
"Because the conditions have changed, because we've changed our plan, we have new standards which we have to uphold," Brunson said.
Seoul has maintained that the transfer should proceed under the conditions previously agreed upon by the allies.
Defense Minister Kang Shin-chul told lawmakers Thursday that South Korea had already conveyed its concerns to the United States over Brunson's OPCON remarks.
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