Lady Sylvia Hermon, the only re-elected Ulster Unionist MP, has said she will consider whether to run for the leadership of the party.
The party is expected to call a meeting of its governing body, the Ulster Unionist Council, to elect a new leader within a month.
Speaking on RTÉ's 'This Week' programme, Lady Hermon said she was committed to the party and the future of Northern Ireland, and will decide in the next few days whether to run for the leadership.
David Trimble stepped down as leader yesterday following the Ulster Unionists' devastating defeat in the Westminster elections.
It has reduced the Ulster Unionists' representation in the House of Commons to one. The DUP now has nine seats.