"Application is dismissed," it said.
The same bench had on December 17 convicted and sentenced 73-year-old Kumar to imprisonment for the remainder of his life in the case and had asked him to surrender by December 31. He had sought more time, till January 30, to surrender saying he has to settle family affairs related to children and property and also needs time to file appeal in the Supreme Court against the high court verdict.
The application, filed through advocate Anil Dharma, had said Kumar was "under shock and surprise" since the time he has been convicted and he believes that he is innocent.
The case relates to killing of five Sikhs in Raj Nagar part-I area in Palam Colony in South West Delhi on November 1-2, 1984, and burning down of a Gurudwara in Raj Nagar part II during that period.
The riots had broken out after the assassination of the then Prime Minister Indira Gandhi on October 31, 1984 by her two Sikh bodyguards.
The high court in its judgement had said that the riots were a "crime against humanity" perpetrated by those who enjoyed "political patronage" and aided by an "indifferent" law enforcement agency.
It had set aside the trial court's verdict which had acquitted Kumar in the case.
The court had said there has been a familiar pattern of mass killings since the Partition, like in Mumbai in 1993, Gujarat in 2002 and Muzaffarnagar, UP in 2013, and the "common" feature of each was the "targeting of minorities" with the attacks being "spearheaded by the dominant political actors, facilitated by the law enforcement agencies".
The six accused, including Kumar who was a Member of Parliament at that time, were sent for trial in 2010. Three years later, the lower court convicted five of the accused but acquitted him of all the charges.
The high court upheld the conviction and varying sentences awarded by the trial court to the other five -- former Congress councillor Balwan Khokhar, retired naval officer Captain Bhagmal, Girdhari Lal and former MLAs Mahender Yadav and Kishan Khokhar.
It also convicted them for criminal conspiracy to burn down residences of Sikh families and a gurdwara in the area during the riots.
The trial court in 2013 had awarded life term to Khokhar, Bhagmal and Lal, and a three-year jail term to Yadav and Kishan Khokhar.
Following the high court verdict, life term of Khokhar, Bhagmal and Lal has been upheld and the sentence of Yadav and Kishan Khokar has been enhanced to a 10 years in jail.
All six, including Kumar, were directed by the high court to surrender by December 31, and not to leave Delhi.