The new leader of the Ulster Unionist Party will be elected at a special meeting of the party's ruling council on 23 June.
Mr Burnside has backed Lord Kilclooney to be interim leader
Until then three prominent members will be in charge - party president Lord Rogan, assembly member Sir Reg Empey and its only MP, Lady Sylvia Hermon.
The decision was made at a meeting of the UUP's executive on Saturday.
David Trimble resigned his leadership after the party lost all but one of its seats at Westminster.
Some party members had wanted to postpone a leadership contest until after the summer but the executive decided it could not wait.
Potential candidates could include Sir Reg, David McNarry or Lord Maginnis, possibly with Basil McCrea.
The party's only remaining MP, Lady Hermon, is still considering whether to run.
She wants the party to head in a more liberal direction.
However, former South Antrim MP David Burnside told Radio Ulster on Saturday he did not think she was up to the job.
"She does not have the presence in the House of Commons, I believe, to be a leader of the Ulster Unionist Party," Mr Burnisde said.
"If the party wants to go off on some sort of softy, wishy-washy, liberal sort of route they'll have a lot of other people who are still in the party stepping aside from it. We don't need to go that route."
Mr Burnside has backed Lord Kilclooney to be interim leader.
It is inderstand he has declared he would like to lead the party until next April.
After losing all but one of its MPs and 40 councillors in the elections, the UUP must decide who should lead the party and what direction it should take.
Lady Sylvia Hermon wants the party to take a more liberal direction
The party lost four of its MPs in the election.
Mr Trimble, the former first minister in the suspended Stormont Assembly, lost his Upper Bann seat.
The UUP now has one MP, compared with the Democratic Unionists' total of nine.