During arguments, the CBI told a bench of Justices Gita Mittal and P S Teji that these pleas should be dismissed as it was an attempt to delay the proceedings.
Kumar and others have alleged in their applications that Justice Teji should not hear the matter as he had heard the case earlier when he was a trial court judge.
Kumar was acquitted by a trial court in 2013 in the case pertaining to the killing of five Sikhs by a mob in Delhi Cantonment's Raj Nagar area during the 1984 riots.
Former MLA Mahender Yadav, who was handed a three year jail term in the matter and is currently on bail, had also alleged that "Justice Teji was exercising keen interest in the matter" and should recuse himself from hearing these appeals.
Earlier, CBI in its reply to Kumar's application had said it was an attempt to cause "obstruction", delay proceedings and frustrate the course of justice.
Besides Kumar and Yadav, convict Kishan Khokkar, who was sentenced to three year in jail and is on bail, has also filed a similar application.
While acquitting Kumar, the trial court had held five accused guilty and awarded them varying jail terms for being part of the mob that killed the Sikhs.
Ex-councillor Balwan Khokkar, Girdhari Lal and retired naval officer Captain Bhagmal were given life term, while the remaining two, Yadav and Khokkar, were given three-year jail term each for their lesser roles. They have also challenged their conviction in high court.
Besides CBI, the victims' family members Jagdish and Nirpreet Kaur had also challenged the trial court order.
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