The funding is being supplied through the Discretionary Housing Payments (DHP) scheme and can be made to households where the local housing allowance does not cover their whole rent, or to families in hardship or struggling with housing costs.
The Scottish Government said it will also support those affected by the UK Government benefit cap or bedroom tax and those requiring a rent deposit.
The scheme comes under full Scottish Government control from Monday.
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Housing minister Paul McLennan said: “This funding will help to bridge the gap between what people need in benefits from the UK Government, and what they actually receive.
“This can be the difference between a family thriving, or a family experiencing financial hardship.
“We are clear that this is the right thing to do to support households – but the Scottish Government should not be forced to step in and divert money from our own housing and anti-poverty policies because of UK Government welfare reforms.”
Satwat Rehman, chief executive of the One Parent Families Scotland charity, said: “The Scottish Government is to be commended for taking these mitigating measures as we recognise it continues to spend massive sums compensating for welfare cuts made the UK Government.
“Mitigating the benefit cap is absolutely the right thing to do. The increased funding and improved support for families affected by the benefit cap will be greatly welcomed by the many single parents who have been pushed into further hardship by this policy.
“Seventy-four per cent of all capped households in Scotland consist of single parents with children – 92% of whom are women.”
The charity has now urged the UK Government to scrap the benefit cap completely.
While responsibility for the DHP scheme was devolved in 2017, the Scottish Government said it was regulated by the UK’s Discretionary Financial Assistance Regulations 2001, with that provision being revoked in April.
A UK Government spokesperson said: “We are spending over £30 billion in 2023/24 on housing support, which includes over £1.8 billion in Scotland.
“In recognition that some households may need additional support with housing costs, the UK Government continues to provide funding for Discretionary Housing Payments, which have been devolved to Scotland since April 2017.”
The UK Government added that the benefit cap ensures the welfare system remains “fair”.
