Mr Robinson said the DUP had proposed a new £27m a year fund to help those with the highest level of disability.
The DUP leader said this would help with the transition from Disability Living Allowance to a new system of personal independence payments.
He said he had put the proposals to Secretary of State Theresa Villiers.
The Northern Ireland Assembly has not yet passed the legislation required to authorise the welfare changes, which are opposed by both Sinn Féin and the SDLP.
Welfare reform remains a key point of dispute in the inter-party talks that began on Thursday.
In a speech in County Down on Friday, Mr Robinson said his party had put forward proposals to the secretary of state “so that people and parties could see what the full picture might look like”.
“Specifically, we now believe that in relation to the bedroom tax, funding would be used to meet the cost of future tenants who are allocated homes that are under-occupied,” he said.
“This would be in addition to the measures already provisionally agreed for existing tenants. It is estimated that this would cost an additional £3m per annum.”
He said the £27m annual fund for those transitioning from Disability Living Allowance would mean “most of those with the greatest need” would either have the same level of payments or be better off.