The group has threatened to start executing the South Koreans abducted five days ago unless Seoul agrees to withdraw its troops from Afghanistan and also make Kabul comply with their demand to free 23 Taliban prisoners.
A Taliban spokesman said the extension was to give time for the South Korean government to open direct talks with the kidnappers.
Earlier on Monday a Taliban spokesman said 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.”
Afghan government troops have surrounded the area where the kidnappers and their hostages are believed to be holed up
The South Koreans, who belong to the Saemmul church in the city of Bundang, outside Seoul, were seized last Thursday.
Eighteen of the hostages are women. Most are in their 20s and 30s and they include nurses and English teachers among their number.
On Tuesday a South Korean foreign ministry official told the Associated Press that the hostages were all believed to still be safe.
The official, who was not named, said Seoul was “maintaining contact”‘ with the hostage-takers and mobilising “effective means” to resolve the crisis.
The South Korean embassy in Kabul said the hostages had been working for an aid organisation in the southern Afghan city of Kandahar, a former Taliban stronghold.
Meanwhile the fate of two Germans and five Afghans taken hostage by the Taliban earlier this month remains confused.
The group had earlier said it had killed all seven hostages, but on Monday a Taliban spokesman aid it had only killed one of the Germans and was continuing to hold four Afghans after one man had escaped.