Ian Paisley is being pushed to explain in public next week why he and Martin McGuinness are months overdue in naming Northern Ireland's new Victims' Commissioner.
Speculation is growing that the two men are unable to agree on the key appointment, one of the first they were to make together.
Yesterday SDLP MLA Dolores Kelly tabled a question about the delay, which the First Minister is scheduled to answer when he appears before the Assembly on Monday.
Monday's meeting will be the first full session of the Assembly since the summer holidays.
Mrs Kelly said victims and survivors of the Troubles "feel let down" by the First Ministers' "dithering".
Almost four months have passed since they were handed a shortlist compiled by the NIO.
The First Ministers' office said they "want to get the decision right" but did not explain the delay.
"We would ask everyone to be patient; the appointment of a Victims Commissioner is under active, detailed and careful consideration and we hope to make an early decision on this important appointment," a statement said.
The £65,000-a-year post - previously held by Bertha McDougall - was advertised in January and 13 people were interviewed in March.
Mr Paisley and Mr McGuinness were given the shortlist almost immediately after they took up office on May 8.
In June, they told the Assembly they planned to announce the appointment before MLAs began their summer break on July 10.
But that deadline passed without an announcement, and their office said that they aimed to make a decision "as soon as practicable".
Reports say that shortlist includes former UTV presenter Mike Nesbitt and Marie Breen Smyth, who used to run the Institute of Conflict Studies in Belfast.
In a statement, the First Ministers' office said they "had hoped to make an appointment before the recess but this did not prove possible.
"Victims and survivors needs are a high priority for us and we want to get the decision on an appointment right. We will take the necessary time to do this.
"Political point-scoring on this issue is both unhelpful and entirely inappropriate, not least to those who have suffered so much during the Troubles."
Mrs Kelly said she is concerned that victims are not getting practical help with "housing, health and counselling" because of the absence of a Commissioner.
"If you talk to people in psychiatry, they say there's been an increase in psychiatric disorders related to the conflict since the ceasefires," she said.
"There are still many people suffering from the pain of losing their loved ones in the Troubles and there are many survivors still searching for truth and justice.
"Nobody's championing their cause and it seems like there's no impetus to look at the real needs of the victims.
"I am outraged that the First and Deputy First Ministers have sat on this issue for so long. Do they not think people have waited long enough, have suffered long enough?
"It's time for Ian Paisley and Martin McGuinness to stop posing for media photographs and start getting down to delivering on the issues that matter.
"I am calling on the First and Deputy First Ministers to give an explanation for their dithering on appointing a Victims' Commissioner. They must announce the appointment as soon as possible so we can start to effectively deal with the past."