The Ulster Defence Association has been warned it must decommission its arsenal if it wants its political wing to keep government funding.
The UDA say they will not give up their guns
Social Development Minister Margaret Ritchie's department is responsible for a policy approved by her direct rule predecessor.
It gives almost £500,000 a year to the Ulster Political Research Group.
The minister said she was alarmed by UDA leaders saying that giving up guns was "not on their radar screen".
"If this funding is to continue, then the UDA have to decommission their arsenal," she said on BBC Radio Ulster's Inside Politics programme.
"An intergral part of the transformation initiative is decommissioning.
"I have already communicated that message to them and I, as the minister, demand that they do that. The public demands that they do that."
A total of £1.2m is being provided by the government over four years.
The Ulster Political Research Group said the money could help transform the UDA into a non-paramilitary group.