The council and STAG have, for the first time, been trying to reach a compromiseÂ over tree felling after years of disputes.
The council signed a Â£2.2bn contract with PFI contracter Amey to improve the city's highways over 25 years, which included a target to fell 17,500 street trees.Â
Over the first five years of the contract the council and STAG have repeatedly clashed leading to arrests of protesters and the council taking members of the group to court for standing in 'safety zones' during works.Â
The first mediated talks between the two groupsÂ tookÂ place on Thursday 27Â September and Friday 28Â September.
They were chaired by the Centre for Effective Dispute ResolutionÂ and overseen by the Bishop of Sheffield, the Very Reverend Dr Pete Wilcox.
In a joint statement from Councillor Lewis Dagnall, cabinet member for environment and streetscene, and Chris Rust and Paul Brooke, co-chairs of STAG, said: 'We have completed two days of constructive, mediated talks, and have made substantive progress over that time.
'We have agreed to meet again in three weeks to continue our talks.
'Both parties are hopeful that we will be able to make a full announcement at that point, covering a proposed approach to completing the remaining period of the Streets Ahead programme, alongside developing our street tree strategy for the future.
'In the meantime the current pause on tree replacement will continue.'
The council's delegation included councillors, council officers and representatives from Amey.
The delegation from STAG included members of the steering committee and a representative of Trees for Cities.