Peter Robinson demanded the meeting in a telephone conversation with Owen Paterson in a bid to have the controversial decision overturned.
“This outrageous decision has been made by the MoD in London without any consultation either with the local administration or local representatives,” the DUP leader said.
“The decision is unacceptable and we will be seeking a review of the decision otherwise the impression will be given that dissident republicans can dictate where our soldiers are able to parade.”
The Royal Irish Regiment will be taking part in an annual service of Thanksgiving at St Anne’s Cathedral on May 22.
However, petitions calling for a full military parade to go ahead have been organised.
Last week the Belfast Telegraph revealed that the MoD had snubbed an invite from Belfast City Council to organise an event in honour of the Royal Irish |Regiment and Irish Guards who have recently completed a six-month tour of duty in Helmand Province.
Defence Secretary Liam Fox, who had previously backed the proposal to have a Belfast homecoming, said it was a “kind invitation” but a parade was “not the best way to proceed”.
“We will consult the city council and other parties in the coming days about how we can best mark their commitment in another form,” he added.
More than 1,500 Northern Ireland soldiers returned from tour in Helmand province just over a fortnight ago.
Three RIR troops, Ranger Aaron McCormick (22) from Coleraine, Ranger David Dalzell (20) from Bangor and Lance Corporal Stephen McKee (27) from Portadown, were killed during the six-month deployment.
Parades are due to take place in Ballymena and Enniskillen next month with the largest event planned for Lisburn on May 21.
North Belfast MP Nigel Dodds said: “The decision by the Army/MoD to turn down the invitation for a homecoming parade in Belfast for the Royal Irish Regiment and the Irish Guards is ridiculous and must be changed.
“The ordinary people of Belfast and Northern Ireland turned out magnificently to welcome home the troops last time.
“The DUP will be seeking to have this MoD/Army decision overturned as quickly as possible.
“We will also be raising the matter with the relevant ministers and also raising it on the floor of the House of Commons in Parliament next week.”
Background
A massive security operation had to be mounted during a military parade in 2008 to keep rival factions of hardline loyalists and dissident republicans apart.
With reference to the latest MoD invitation, republican splinter group eirigi had vowed to “actively oppose” the march.