Sir Marcus, 68, said he will fight any attempt to unseat him from the committee chairmanship and vigorously denied reports that he will not be contesting the general election.
Mr Dunn, 49, is one of the few long-serving members of the 1922 Committee who is standing at the next election, and he is basing his campaign on the need for continuity.
Mr Dunn's challenge - forecast in the Independent last Thursday - will mark the start of a clear-out of "grey suits", the elderly knights of the shires who pass on backbench opinion to the leadership.
Eight members of the executive are standing down at the election. They are Dame Jill Knight, Sir John Hannam, Sir Peter Hordern, Sir Giles Shaw, Sir Anthony Durant, Sir Terence Higgins, Sir Fergus Montgomery and Sir Anthony Grant.
But there has been growing dissatisfaction on the backbenches that the officers of the 18-strong1922 Committee - in effect the shop stewards for the Tory backbench - have been passing on leadership views to the rank and file, rather than warning John Major and senior colleagues of their views.
It is expected that if Sir Marcus carries out his threat to stand and fight, he will be run very close by Mr Dunn but there will be challenges to other members of the executive, including Sir Geoffrey Johnson Smith.
Mr Dunn said : "I am standing on one ground and one ground alone. It is now clear that a significant number of the officers and members of the current executive committee will not be seeking re-election at the next general election. "I believe it to be essential that the leadership of the 1922 Committee should be drawn from among those who aspire, subject to the will of the people, to be present in the next Parliament.
"Accordingly it is for reasons of continuity and the need for a succession to be created that I put my name forward as candidate for the chairmanship of the 1922 Committee."
Sir Marcus was accused of shooting from the hip during the leadership election, when he appeared to offer the endorsement of the executive for John Major. That angered at least two members of the executive, David Evans and John Townend, who supported John Redwood.
The 1922 Committee chairman also surprised colleagues recently by saying there was a case for stealing Labour's clothes by imposing a windfall profits tax on the privatised utilities to pay for tax cuts.
Sir Marcus is a gritty fighter who last year saw off a challenge by Sir Nicholas Bonsor. Sir Nicholas was made a foreign minister after Mr Major's leadership election.Reuse content