The Ulster Unionist MLA Basil McCrea has said party leader Sir Reg Empey should stand down now.
Sir Reg has already announced that he intends to stand down in the autumn.
It follows the UUP's disappointing results in the general election where they failed to win any Westminster seats.
Mr McCrea, who is viewed as a possible contender to replace Sir Reg, says the party needs to elect a new leader as soon as possible.
"There's a general rule that whenever people decide that they're going in any walk of life, that if you don't go soon, what you end up with is a lot of discussions," he said.
"They become increasing fractuous as time goes on and frankly, it does no good to either the incumbent leader or the party itself.
"The party really needs to get to grips with issues, about what it stands for, what its vision is.
"The best way of doing that is to have a leadership election."
In the general election, Sir Reg chose to stand in the South Antrim constituency, which was thought to provide the party's best chance of making a gain from the Democratic Unionists.
However, he lost out to the DUP's sitting MP, William McCrea.
The only UUP MP remaining after its disastrous 2005 general election performance, Lady Sylvia Hermon, left the party to stand as an independent in protest at its link-up with the Tories.
She retained her North Down seat with a convincing majority.
The UUPs 100-strong party executive met after its electoral pact with the Conservatives failed to secure any Westminster seats.
It is believed party colleagues had urged him to stay on but Sir Reg said it was the right time for him to quit.
The UUP has also decided to hold a review of its relationships with other political parties, including the Tories and the DUP.
It will be led by the party's vice chairman Terry Wright, who will oversee the review of its operations and recent failures.