Ian Davidson, who chairs the Commons' Scottish Affairs Committee, said the SNP administration had taken too long to address the impact of the controversial UK welfare reform policy, which cuts benefit payments for people deemed to have a spare room.
The Glasgow South West MP's call comes less than a week after Scottish Finance Secretary John Swinney announced he was topping up a fund to £50 million so he could offset the benefit cut.
Mr Davidson spoke out after visiting West Lothian, where his committee of MPs heard half the council tenants were in arrears.
Concerns were also raised that simply addressing debt would "penalise" those who scrimped and saved to pay their bills.
"All of these problems have been created by the Scottish Government's delay," he said. "Households and councils have been left to deal with it at great personal and administrative expense. The Scottish Government has the power and the money to resolve this mess. The only question is why they haven't."
Dr Eilidh Whiteford, the SNP's work and pensions spokeswoman, said: "The best way to mitigate the impact of the bedroom tax is to make payments directly to the individuals affected. If the Scottish Affairs Committee wants to do something useful it should be backing Scottish Government calls for the cap to be lifted."