Bristol City Council has said that further surveys to investigate the condition of the city's oldest tower block, Barton House, will start "imminently".
It comes as some affected residents are being asked to move hotels as the council tries to secure rooms for the "foreseeable future".
More than 400 people - including around 100 children - were told to pack a bag of clothes and leave on the evening of Tuesday 14 November.
They were given less than five hours to evacuate the block of 98 flats after surveys flagged a “risk to the structure of the block”.
As of Tuesday 21 November, 69 households were still in in hotel accommodation, 13 were staying with friends and family and 10 remained at Barton House.
The council said two flats had been found empty and no households have moved back into the building since leaving.
Marvin Rees, mayor of Bristol, has admitted it will be at least two weeks before they can update Barton House residents about their future in the building.
Mr Rees said that the next round of survey results would indicate if residents could ever return.
His comments came hours after hundreds of protesters gathered at City Hall demanding answers from Bristol City Council and clarity on their future.
The surveys beginning will see a small amount of furniture and possessions removed from those flats so they are not damaged. The council says the tenants of these flats have provided written consent for this to happen.
Some 200 people are currently living in three of the city's hotels and the council says it has made arrangements to secure more rooms at The Holiday Inn on Bond Street for the foreseeable future.
In a statement, it said: "After working with management at the Holiday Inn (Bond St), arrangements have been made to secure more rooms at the hotel for the foreseeable future.
"During the course of this week, residents currently residing in Leonardo Hotel and Clayton Hotel will be supported to move into the Holiday Inn (Bond St).
"This move will provide residents with more certainty about their short-term accommodation arrangements and ensure all support services can be provided from one location, cutting out the need to travel between hotel locations.
"Residents at Leonardo Hotel have moved today (Monday 20 November) and those at Hotel Clayton will be supported to move tomorrow (Tuesday 21 November).
"All residents at Clayton Hotel have been contacted to advise of the move and transport options are in place to help.
"Whilst we recognise the additional stress and discomfort these moves will cause residents, there is no further availability at the hotel from Tuesday evening."
A free helpline is available and will be open over the weekend to take any calls from residents of Barton House – 0800 694 0184.
Community Access Support Service can help you find organisations across Bristol for all groups of people and communities – www.cassbristol.org
Samaritans offer support 24 hours a day, 7 days a week – call 116 123 for free.
Shout 85258 offers confidential text support 24 hours a day, 7 days a week. Text SHOUT to 85258.
Family Hubs: during the week, your local Family Hub can give you information and support about anything relating to you and your family. This includes activity groups, health and wellbeing services and parenting support. The nearest Family Hub to Barton House is the Wellspring Settlement Hub, 43 Ducie Road, Bristol, BS5 0AX. It is open from Monday to Thursday, 9am to 4.30pm, and on Friday from 9am to 1pm. You can call them on 0117 955 6971.
Support for mothers with babies and infants: The Central Children’s Centre will be running “stay and play” baby groups at the Holiday Inn. Details of this will be shared in future communications. There is information above on how to book a free taxi to the Holiday Inn when needed.
Welcoming Spaces network: Welcoming Spaces are still open across the city. These are free to use and open to anyone. You can use your local Welcoming Space to meet with other people, take part in activities or access support. Find your nearest hub here.