A bench headed by Chief Justice G Rohini dismissed the appeal of Vikas, who had sought further three weeks after he was granted one week parole by a single judge bench of the high court.
"In the facts and circumstances of the case we do not find any error requiring interference in the discretion exercised by the single judge in refusing the three months parole sought and in granting only one week of custody parole," it said.
The bench, also comprising Justice R S Endlaw, observed that grant of parole is essentially a discretionary act though the discretion is to be guided by a number of facts.
"The settled principle of law is that in exercise of letters patent jurisdiction,the division bench would interfere with the discretion exercised by the single judge only if it is perverse and not to substitute its own view over that of the single judge," it said.
The court also said the single judge had given well founded reasons for granting one week's custody parole to Vikas and it was free from "perversity or illegality".
On April 20, the high court had reserved its order on Vikas' plea seeking three weeks of parole for the preparation and filing of a special leave petition in the Supreme Court against the conviction and sentence awarded by the high court.
The bench had fixed on Wednesday for passing the order after the counsel for Vikas and Delhi Police concluded their arguments.
The counsel for Delhi Police had vehemently opposed Vikas' plea for parole extension, saying the court has granted enough time to the convict to prepare his appeal.
A single-judge bench had on April 10 refused to extend the parole of Vikas and asked him to "surrender immediately".
Vikas, son of Uttar Pradesh politician D P Yadav, sought 21 more days for him to surrender, saying he was not able to prepare the appeal, for which he was out.
The convict was granted seven days parole last month, after he said he wanted to challenge in the Supreme Court, the high court verdict in the murder case and wanted to prepare for it.
The high court had on February 6 enhanced the sentence for Vikas and his cousin Vishal from life imprisonment to 25 years without remission for the murder of Nitish Katara and five more years for destruction of evidence in the case.
The convicts' acquaintance Sukhdev Yadav, alias Pehelwan, was also awarded an enhanced life sentence of 20 years without remission by the high court.
The three were awarded life term by a trial court for abducting and killing Katara, a business executive and son of an IAS officer, on the intervening night of February 16-17, 2002. They did not approve of the victim's affair with Bharti, the daughter of D P Yadav.
The high court had on April 2, 2014, upheld the verdict of the lower court in the case by describing the offence as "honour killing" stemming from a "deeply-entrenched belief" in caste system.