James Bays, Al Jazeera's correspondent in Afghanistan, cited a Taliban spokesman as saying tribal elders mediating between the Taliban and government officials had not had time to complete talks which broke down earlier in the day.
A Taliban spokesman had earlier said that the South Koreans were in good health, but added that negotiations with Afghan and South Korean officials were "not going well".
He said: "They are in good health and fine, but ... any use of force will claim the lives of the hostages and the Taliban then would not be responsible."
The South Koreans, who belong to the Saemmul church in Bundang, a city outside South Korea's capital, Seoul, were seized last Thursday.
Most of them are in their 20s and 30s, and include nurses and English teachers.
An anti-war rally near the US embassy in Seoul on Monday called for the safe return of the hostages and the withdrawal of 200 South Korean soldiers from the country.
Bays said the Taliban had also said they had only killed one of two German hostages taken captive earlier this month.
The group had previously said it had killed both.
The Taliban also said that four Afghans taken hostage with the Germans were still alive and that a fifth had escaped.
The group had earlier said that they had all been killed.