The owners of Guildford Crescent have agreed to postpone their plans for demolition following a meeting with the local council.
The future of popular music venue Gwdihŵ and neighbouring restaurants were cast into doubt last month after it was announced the landlords decided not to renew its lease.
Restaurants Thai House and Madeira had also been told they must leave their premises by the end of the month.
Cllr Thomas said: "Following a constructive meeting with the landowners they have now agreed to put their demolition plans on hold while consideration is given to development opportunities in the wider area.
"During our discussions I urged the landowners to reconsider their position regarding the termination of business leases held by the current tenants of Guildford Crescent while our talks continue. While the tenancy arrangements are out of the Council's hands, we have re-emphasised the importance of these businesses to this area and their value to the identity of the city.
"The Council is very aware of the public concern caused by the potential loss of the Madeira restaurant, The Thai House and the independent, music venue Gwdihŵ and we are actively working with Gwdihŵ to help them relocate in the city if the need arises."
Cadw, which listed the Masonic Lodge on the Crescent in 1975, is currently undertaking an assessment to see if the rest of the buildings on the Crescent should be listed.
Cllr Thomas added: "The creation of a conservation area is a completely distinct matter. That decision has to be taken based on the architectural or historical significance of the area, the character or appearance of which is desirable to preserve or enhance. We are continuing to investigate the viability of such an order.