Zabihullah Mujahid, the spokesman for the militant group, told media outlets on Friday that the discussions were informal and cannot be categorized as "peace talks."
Afghan government sources say members of the government's High Peace Council are also in Norway for the talks.
Local media reports say Afghan female lawmakers Shukria Barekzai and Fawzia Kofi and some civil society members are reportedly among the participants.
Sources on both sides have said that the meeting could be a step toward opening further talks to end the decades-long conflict in Afghanistan.
The meeting is the latest face-to-face talks between Afghan government officials and Taliban and in recent months.
Afghan government has held talks with the Taliban militant group in the Qatari capital, Doha, in recent months.
Some media reports had earlier indicated that Pakistani negotiators have also been persuading the Taliban leadership to embark on peace talks with the Afghan government and the Americans.
In 2010, former Afghan President Hamid Karzai established the peace council in an attempt to negotiate peace with the Taliban. Previous efforts by the Afghan government to reach a deal with Taliban militants have been fruitless.
In June 2013, the Taliban opened an office in Doha, but closed it a month later. However, the Taliban office was revived again in February 2015.