The Scottish Parliament Welfare Reform Committee has written to the UK Work and Pensions Secretary over the number of people applying for help to meet rent payments following a benefit cut from the 'bedroom tax'.
Mr Duncan Smith met in private with committee members earlier this year, but refused to give evidence in a formal, public session.
Instead DWP officials appeared before the committee, with their comments on benefit changes branded "claptrap" by one MSP.
The committee said it has fears that if Discretionary Housing Payments (DHP) are stopped, councils will be unable to cope with the increase in applications for help.
Committee Convener Michael McMahon has invited Mr Duncan Smith to Holyrood, expressing his disappointment that he has so far refused.
He said: "I am very concerned that if there is no guaranteed continuation of DHP funding at a similar level in the next financial year, local authorities will not be equipped to meet the demand for payments."
The committee has called for the same funding for this year to be available next year and for an announcement to be made to allow councils to plan ahead.
The committee earlier this year heard from South Lanarkshire Council, which said that there had been an increase of 425% in the number of people seeking DHP.
The council told MSPs there were 3868 tenants affected by the 'bedroom tax', and 1639 had arrears from the benefit cut.
Mr Duncan Smith previously declined an invitation to appear by stating that, as welfare was a matter reserved to Westminster, he was accountable only to the UK Parliament.
Mr McMahon added: "I, along with other members of the committee, remain very disappointed that, to date, you have refused to appear before the committee in public.
"I feel the issue of DHP funding levels, the operation of direct payments and your recent announcement of the postponement of the implementation of Universal Credit are issues which would benefit from public discussion."
In May, Pete Searle, Strategy Director of DWP appeared with two colleagues, where he said people can take in a lodger, get a job or move to avoid the bedroom tax.
Kevin Stewart, SNP MSP told him he was talking "claptrap".