Alex Salmond will raise objections to the UK welfare reform with David Cameron at a meeting of the heads of the UK administrations on Wednesday.
The under-occupancy charge, described as a bedroom tax by opponents, will cost the average tenant £54 a month extra if they do not fill the room or move to a smaller property.
Those affected can apply for discretionary housing payments to help with their rent in some circumstances, including those in disabled-adapted homes or in an area with a shortage of shared accommodation.
The Joint Ministerial Committee (JMC), which comprises the UK Government, the Scottish Government, the Welsh Government and the Northern Ireland Executive, meets once a year.
Scottish Youth Employment Minister Angela Constance will accompany the First Minister to this week's session.
A Scottish Government source close to the First Minister said: "The bedroom tax is a deeply unfair, deeply unpopular policy, and its full effects are now becoming clear in communities right across Scotland.
"Now that we have the evidence of just how damaging the bedroom tax is, the Tory-led UK Government must listen.
"It is a punitive measure, affecting some of the most vulnerable in our society, and it must be scrapped, something the First Minister will make clear to the Prime Minister when they meet this week.
"A Yes vote next year will give us the opportunity to do that, and we are committed to scrapping the bedroom tax if we form the first administration of an independent Scotland."
Scottish Conservative welfare spokesman Alex Johnstone said:"The SNP has cynically used changes to welfare and benefits as arguments for separation but have refused to lay out what kind of welfare system there would be under independence and how it would be funded.
"For Alex Salmond to try and make this a head-to-head issue with him and the Prime Minister is just another diversionary tactic to get away from the fact he and his party are all over the place on welfare."