"We are trying to find a solution. Contacts between the Taliban and the Korean ambassador are going on over the phone," he said.
The Taliban have killed two of the hostages and have repeatedly threatened to kill the remaining 18 women and three men unless the Afghan government agrees to free prisoners in exchange.
Afghanistan has refused to release Taliban prisoners, saying that would encourage a kidnapping "industry".
"We will not do anything that will encourage hostage-taking, that will encourage terrorism. But we will do everything else to have them released," Hamid Karzai, the Afghan president, told CNN ahead of a visit to the US where he is holding two days of security talks with George Bush, the US president.
South Korea has proposed holding face-to-face talks with the Taliban as a way of breaking the impasse, but a new apparent deadlock has emerged over where to hold the talks.
Taliban kidnappers have demanded the meeting take place in territory they control or under a UN guarantee for their safety if held elsewhere. But after four days of talks on where to hold negotiations, there were few signs of progress.
A UN spokesman said the international body has not received any request from the Taliban to supervise or guarantee talks.
South Korean officials in Afghanistan meanwhile made their first contact with one of the hostages, an official in Seoul said on Monday.
"There was a telephone conversation with one hostage on Saturday afternoon," said a South Korean official on condition of anonymity.
The official declined to give further details, citing a potential risk to the safety of the hostages.
In Seoul, about 150 demonstrators rallied at the US embassy, praying for the hostages' release and demanding US help.
Peace activists and members of anti-American political parties said the captives are victims of South Korea's military alliance with the US and held banners which read: "Withdraw the US army from Korea" and "Abolish the Korea-US alliance."
The United States has around 28,000 troops stationed in South Korea.