UNAMA said this on Twitter after its officials met with the Taliban political commission in Qatari capital Doha.
UNAMA said that reduced violence is required to improve atmosphere for negotiations. It said that UN underscored its availability to give expert help to the peace process.
Intra-Afghan talks were originally scheduled to begin on March 10 as per the deal between the United States and the Taliban.
However, the talks were delayed due to disagreement over the prisoner release which is required in the deal as confidence building measure.
Afghan government has released 4,680 out of 5,000 prisoners the group is demanding.
Meanwhile, US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad on Sunday called on all sides to accelerate the peace process and start intra-Afghan negotiations as soon as possible.