The IRSP has said delays in registering the party for May's assembly elections could disenfranchise its voters.
Earlier this year the party announced that it is due to stand candidates in the assembly elections for the first time.
Dan Murphy in west Belfast and Collie McLaughlin in Foyle have so far been confirmed.
It has now emerged that the Electoral Commission has rejected the IRSPs application to register as a party.
The IRSP last night claimed that registration papers were submitted to the Electoral Commission on January 20 and that two months passed before the party was told its application had been rejected.
The party claims that an older version of its constitution, which it claims was previously accepted, was attached to the application in error. It says that within hours, the required document was submitted but that it was told last week a new application was required.
The party also claims it has been told any reapplication to register would be too late to meet the election nomination deadline of April 8.
Party spokesman Michael Kelly, who is Dan Murphy's election agent, said: "We reject their assertion that there is any real logistical barrier to their accepting our constitution between now and April 8 and should they fail to make reasonable moves to rectify the situation, we can only assume that our party and our supporters, will have been deliberately disenfranchised by delay."
A spokesman for the Electoral Commission said: "The proposed constitution submitted by Irish Republican Socialist Party did not met the legal requirements so therefore the application had to be refused.
"The party has now resubmitted its application and provided a new constitution for consideration. We will assess it accordingly and take a decision on all aspects of the party’s application in line with the legal requirements."
The spokesman said the commission tries "to process registration applications as soon as possible" and "that this process can take some time in order to ensure the commission reaches a fair conclusion within the legislative requirements".
