Ian Davidson, who chairs the Commons' Scottish Affairs Committee, said the SNP administration has taken too long to address the impact of the controversial UK welfare reform policy, which cuts the amount of benefit people can get if they are deemed to have a spare room.
His call comes less than a week after Scottish Finance Secretary John Swinney announced he is topping up a fund to £50 million so he can offset the benefit cut, known as a tax by its opponents.
Mr Davidson spoke out after visiting West Lothian, where his committee of MPs heard half the council tenants are in arrears.
Concerns were also raised that simply addressing debt will "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.
"We now know that they could have addressed this at any time since the bedroom tax was introduced but as they did not, 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.
"They should now announce a scheme to meet all the bedroom tax charges for Scottish tenants, write off all the arrears, and refund all the payments that have been made."
Constructive talks between Labour and the SNP at the Scottish Parliament ended with Mr Swinney's deal as part of his budget for the year ahead.
Shifting the money to deal with the Tory-Liberal Democrat welfare policy comes at the expense of spending in other areas, he warned MSPs.
"This is about mitigation - about picking up the pieces from Westminster's iniquitous policy," he said in a debate on his budget.
"The only real solution is to scrap the bedroom tax altogether, and this government believes the only way to do that is for this Parliament to have the full powers over welfare in Scotland.''
Wider problems with the limited number of smaller houses have also been identified.
Mr Davidson's committee heard that 500 households in West Lothian have tried to downsize to avoid being hit by the benefit cut.
"Because of this shortage of suitable housing, at the present rate of transfer, it could take 10 to 15 years to allow all the tenants who wished to downsize to do so," he said.
The SNP wants to tackle the impact of the welfare reform by finding a way around rules imposed by the UK Department for Work and Pensions (DWP). The rules set a £22.85 million cap for discretionary housing payments, which can be used to support tenants at risk of falling behind in rent and getting into debt.
Dr Eilidh Whiteford, the SNP's work and pensions spokeswoman, said: "The Scottish Parliament has agreed that 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 and acting in Scotland's best interests.
"Scottish Labour concede that the UK Government has caused misery for some of the most disadvantaged people in Scotland due to the bedroom tax, yet Scottish Labour's MPs still pretend we are better together as part of the Union.
"The Scottish Parliament uniting last week to reject the hated bedroom tax is proof that we need a 'yes' vote. Only independence can ensure we get rid of it once and for all."