The North Belfast MLA was speaking after the Arm na Poblachta dissident group made the threat against relatives of PSNI officers and staff.
“This reprehensible warning is rightly being condemned by political representatives right across the community and that is welcome,” said Ms McAllister.
“However, this despicable threat should be removed immediately. These people have repeatedly been rejected by the people of Northern Ireland, who do not want to see our society dragged back into the dark days of our past.
“Those thugs behind the threat are not welcome here and they need to realise that. Whatever they believe they are doing for whatever cause it is, they need to know it will not get them anywhere, particularly as it follows the recent attempted murder of DCI John Caldwell in Omagh and the public outcry at that.
“Alliance stands fully behind the PSNI, its officers and staff, who are doing their job every day to protect everyone in our community. If anyone has any information on the criminals making these threats, I urge them to pass it on to authorities immediately.”