Ms Nokes met council leader Susan Aitken to discuss the rolling lock change eviction process for those not given refugee status proposed by asylum seeker accommodation provider Serco.
Serco, contracted by the Home Office, announced a temporary reprieve on the plans last week in the face of legal challenges and protests.
Following the “constructive” meeting, Ms Aitken said: “There is currently little clarity about the actual status of the 330 people affected, therefore it is essential that Glasgow City Council has the time and opportunity to carry out individual assessments for all of them and ensure that everyone gets the right support and outcome for their circumstances.
“The minister agreed this was necessary and her officers have committed to engaging constructively with us to ensure this is put in place.
“Ms Nokes and her officials have been left in no doubt that lock changes and evictions are not good for anyone, and do not have support within the city.
“Whilst she was unable to give a guarantee that they would not continue, we have made significant progress.
“However, we will continue to join with partners across the city to campaign for this policy to be changed.”
The minister is due to meet Serco later and the Scottish Government on Wednesday.
After Serco announced the lock change plans last month, Ms Aitken wrote to Home Secretary Sajid Javid warning it risks a “humanitarian crisis”, leaving those affected out on the streets.
Serco denies the claim and said it currently pays accommodation for 330 asylum seekers who no longer receive Home Office support.
About a third have been granted leave to remain while the remainder have been refused refugee status.
Serco eviction plans affect the latter group, which the firm says have no right to remain in the UK.
Scottish Labour leader Richard Leonard has written to Ruth Davidson, urging her to “break her silence” on the issue and put pressure on the government to halt the evictions.
In response, the Scottish Conservative leader said she met Serco chief executive Rupert Soames last week to discuss the eviction proposals.
She endorsed statements from leader of the Conservative group on Glasgow City Council, David Meikle, calling for clarity and a solution to the “potential crisis”, and from Tory MSP Adam Tomkins.
Mr Tomkins said “if people whose applications have been rejected are housed indefinitely, that is manifestly unfair to others with genuine asylum claims”.