There are reports that the Taliban's political leader Mullah Abdul Ghani Baradar and other leaders are expected to arrive in the capital Kabul either today or tomorrow.
Baradar was among several members of the Taliban's senior leadership who returned home on Tuesday. They had travelled from Qatar to the southern Afghan city of Kandahar, their spiritual birthplace.
Baradar, one of the founding members of the Taliban, had been part of the negotiations with the US in Qatar after being released from prison to help facilitate the peace process.
He was captured in a joint US-Pakistani operation in Karachi in 2010.