"Our stance: Implementation of Doha Agreement & start of intra-Afghan negotiations are necessary so we can work towards de-escalation & end of the war. If anyone seeks ceasefire before talks then such is illogical. War is raging precisely b/c we have yet to find an alternative", Zabihullah Mujahid wrote on Twitter.
He accused the government of creating "obstacles" to negotiations.
"The prisoner exchange process must be completed and intra-Afghan negotiations launched immediately. This is the most correct and reasonable path towards a resolution", the spokesman added.
Earlier in the day, Afghan presidential spokesman Sediq Sediqqi urged the Taliban to stop violence and genuinely join a peace process.
Though the United States and the Taliban struck their long-awaited peace deal in late February, clashes between the government forces and the radical movement continue. Direct intra-Afghan talks were initially scheduled to commence in March but were pushed back due to disagreements over the mutual release of prisoners.
* Taliban is a radical movement, banned in Russia