In an order dated April 20, the poll panel said as both the parties - E Madhusudanan and two others, respondents VK Sasikala and another) had asked for additional time for filing documents and affidavits, it had considered the requests and given them till middle of June to do so.
It also said both groups cannot use the party name AIADMK or the 'two leaves' symbol reserved for the party.
The AIADMK split into two after the death of former Chief Minister and party General Secretary J Jayalalithaa. One faction is led by now jailed Ms Sasikala and the other by former Chief Minister O Panneerselvam.
Prior to the bye-election in the RK Nagar assembly constituency, the Election Commission froze the party name and the symbol.
It permitted Panneerselvam group to be called as AIADMK-Puratchi Thalaivi Amma and allotted it the 'electric pole' symbol for the by-poll, while the Sasikala group was called AIADMK-Amma and was allotted the 'hat' symbol.