Renfrewshire Council says the money will be available via a new council tenant assistance fund to help people who are strugg-ling to pay their rent.
Councillor Tommy Williams, convener of the housing and community safety policy board, said: "Between April and July, 684 council tenants applied for discretionary housing payment to assist them with their housing costs, with the majority of those affected by the 'bedroom tax'.
"But while many have come for support, there are still tenants who are struggling to pay their rent because of 'bedroom tax' who haven't come to us for help.
"We have already said that we won't evict our tenants who fall into arrears as a result of the bedroom tax, as long as they are working with us, and we want them to know that this assistance fund is now available to help them cope with the strain of under occupancy.
"We absolutely do not want local families to face hardship because of the bedroom tax and we will continue to work with our tenants to help them."
To apply to the fund, visit www.renfrewshire.gov.uk/dhp or call 0300 300 0204.
It was agreed to create the fund at yesterday's housing and community safety policy board.