The DUP has said it wants a meeting with Tony Blair over the decision to disband units of the Royal Irish Regiment.
The RIR's NI-based battalions are to be disbanded
The Northern Ireland-based battalions of the regiment are to be disbanded on 1 August 2007, as part of the response to the IRA ending its armed campaign.
The Army will end its support role to the police on the same day.
The DUP will press Secretary of State Peter Hain on the implications of the decision when they meet on Wednesday.
On Monday, Northern Ireland Secretary Peter Hain set out a two-year plan on demilitarisation which he said would be contingent on the security situation.
Unionists reacted angrily to the move, which nationalists have welcomed.
Speaking on Tuesday, DUP assembly member Ian Paisley Jr said the government had acted too soon.
"The policy was that there would be no normalisation structures put about until there were acts of completion," he said.
"Those acts of completion have not taken place. There has been nothing to verify that the IRA has done anything other than issue another statement.
"We want to see the government holding to the position that there must be actions, not words."
However, Sinn Fein leader Gerry Adams said the DUP's threat to delay the political process and talks with his party in protest at the decision to disband the home battalions presented a challenge to the British government.
The Sinn Fein president said there was "no logic" in the DUP's position, and asked if party leader Ian Paisley would prefer the IRA not to have taken last week's initiative.
More than 3,000 soldiers serve in the three battalions, many part-time.
News of the decision was broken to them on Monday morning.
Under the security normalisation plans, Army observation posts will be closed and police stations will be defortified.
Mr Hain also announced on Monday that troop levels in the province would fall from 10,500 to 5,000 in two years time.
The government also aims to repeal within two years counter terrorist laws particular to Northern Ireland if everything goes according to plan.
Twenty-six Army sites out of 40 across Northern Ireland will be closed.
On Tuesday, work began on dismantling the observation post on the top of Divis tower in west Belfast.