The tribunal headed by Justice G P Mittal had in July issued an advertisement calling for responses from the LTTE and any other persons on the review of the ban on the group.
The LTTE has been banned for a further five years under the Unlawful Activities Prevention Act by the central government.
While Vaiko, known for his vocal support for Tamil people in Sri Lanka and the LTTE, was allowed to present his arguments in the matter, his impleadment application was dismissed.
The tribunal will now examine the evidence brought before it by the central government and the government of Tamil Nadu before giving its opinion on whether a five-year ban on the group under the UAPA is correct.
The tribunal will now hold its hearing in Chennai on September 26 and 27, giving an opportunity to any person belonging to LTTE to appear and give evidence on why the ban on the organisation should not be upheld.