Deputy First Minister Nicola Sturgeon said yesterday she was "more than willing" to allocate the additional funds in next financial year's budget, which MSPs are due to consider tomorrow.
The cash would take to £50m the amount available to help people whose housing benefits have been reduced because they are deemed to have surplus bedrooms.
Housing charities have estimated that £50m per year would be required to offset the benefit cuts fully and effectively abolish what is known as the bedroom tax. Ms Sturgeon yesterday asked the UK Government to change the rules to allow the extra £15m to be spent on discretionary housing payments (DHPs), a way of directly compensating tenants who are struggling to pay their rent because of the bedroom tax.
The Scottish Government has already promised £20m for DHPs next financial year - the maximum allowed under housing benefit rules - to top up £15m allocated by the Department for Work and Pensions.
However, ministers are considering alternative ways to support tenants if the UK Government refuses to lift the cap on DHPs, and are not expected to withdraw the £15m.
Ms Sturgeon said: "We are more than willing to put in the extra £15 million, which would increase the amount of help available to a total of £50 million.
"If Westminster lifts the legal cap - which they can easily do - we will be able to help the 76,000 people in Scotland who are suffering from this cut.
"In order to make this legally possible Westminster needs to lift the cap for Scotland and UK ministers should act now."
In a sign the cap is unlikely to be lifted, a spokeswoman for the DWP suggested there was insufficient demand for extra financial support, with £15m of extra help currently unclaimed.
But Scottish Government sources confirmed ministers were still "looking to do more" and were seeking an alternative method to channel the £15m to struggling tenants if the DWP refused to change the rules.
Scottish Labour and the STUC welcomed Ms Sturgeon's move as confirmation that, one way or another, the bedroom tax would be effectively abolished as part of Finance Secretary John Swinney's budget.