The DUP want nationalist involvement in the governance of Northern Ireland but its deputy leader Mr Peter Robinson this evening said anyone linked to terror groups must be excluded.
There can be "no halfway house" between terrorism and democracy, Mr Robinson told a Conservative Party group in London this evening.
He said his party had no "wish to exclude nationalists from having a role in governing Northern Ireland", but he added: "We cannot accept those who are linked to active terrorism ruling over those they continue to terrorise.
"Those who support or engage in such activity exclude themselves from the democratic process."
In an address to the Monday Club, the East Belfast MP repeated colleague Mr Gregory Campbell's claim earlier this week that the DUP would force a renegotiation of the Belfast Agreement after the next Assembly elections by opposing the election of First and Deputy First Ministers at Stormont.
Mr Robinson said his party would approach any negotiations on the basis that the outcome was "a settlement - not a process".
He said: "We are not signing up for a transition into a united Ireland as the Ulster Unionist Party has done. Nor will we sign up for any agreement while a side door is open to the IRA to make secondary deals on an ongoing basis with the Government that tips the balance of the original deal and undermines the nature of such an agreement."
The DUP deputy leader told the Monday Club the Agreement was "fundamentally flawed" and rewarded paramilitaries for their violence, demanding little in return.
PA