"I am well aware of territorial disputes in the South China Sea, as well as the (Dokdo) issue that South Koreans have a high interest in," Ban said.
"I hope the countries concerned resolve such conflicts via dialogue," he said in Seoul after attending the launch of South Korea's first public-private coalition for effective foreign aid.
Ban refused to comment further on the sensitive issue, saying only that "a U.N. chief is not in a position to express his stance on such territorial issues," a report by South Korean news agency Yonhap said.
Ban's appeal comes after the latest diplomatic and verbal wrangling between the two countries.
South Korean President Lee Myung-bak made an "unprecedented" visit to the islands last week, Yonhap reported. He became the first South Korean president to set foot on the rocks.
"Dokdo is the end of our territory. Please make sure to defend Dokdo well," Lee said during his 70 minutes on the island where he visited a police unit.
"Dokdo is indeed our territory and a place worth staking our lives to defend. Let's make sure to safeguard (the islets) with pride," he said.
Immediately afterward, Japan recalled its ambassador to Seoul and lodged a formal complaint with the South Korean ambassador in Tokyo.
The Dokdo Islands are a group of two main islets rising to nearly 560 feet and surrounded by dozens of sharp rocks protruding from the sea.
As with many disputed South China territories, they go by several names, depending on who is claiming them. The Dokdo islands are sometimes called the Liancourt Rocks and known by the Japanese as Takeshima.
Disputed territories also described as lying in differently named "seas," again depending on who is making the claim.
The volcanic rock islands of Dokdo are 46 acres in area and are slightly closer to mainland South Korea, around 135 miles, than Japan, 155 miles. The nearest land mass is South Korea's Ulleung-do Island, about 55 miles away.
Like many disputed islands in the South China Sea they have little use as an inhabitable area and offer some appeal as an ecological point of interest.
Their real value lies in the accompanying ownership of the surrounding sea because of fish resources as well as oil and gas deposits on the seabed.
From time to time members of the public or well-known figures in national life will create stunts to bring their country's ownership claims to the attention of the media internationally.
This week South Korean singer Kim Jang-hoon along with several dozen other protesters began a 3-day relay swim from the Korean Peninsula to the islands.
Also this week a group of Chinese activists set sail from Hong Kong the Senkaku Islands, calling for an end to "Japanese militarism," Kyodo News reported.
The islands are known as the Senkaku to the Japanese, while the Chinese call them Diaoyu.
Action Committee for Defending the Diaoyu Islands will be joined at sea by two other vessels, said Chan Miu-tak, the leader of the group.
Countries with competing territorial claims in the South China Sea include Brunei, Taiwan, Malaysia and the Philippines and China, which claims most of the territories throughout the sea.
What limits discussions or stalls talk for many of the countries is whether to go to the International Court of the Justice in The Hague.
China, in particular, insists on bilateral talks with no negotiations through third parties.
South Korea also insists the Dokdo dispute shouldn't be taken to the ICJ.
"The reason why the Japanese side is considering filing a suit with the International Court of Justice is to make the Dokdo issue an international dispute," a government official told Yonhap last week.
"Our government's basic stance is that we will not accept it because Dokdo is clearly our territory," the unnamed official said.
2014: The Year in Music [PHOTOS]