Lawyers for Robert Rodgers claimed he should have been granted the pardon because he has already served nearly 17 years in prison for another sectarian killing in the 1970s.
But a judge on Thursday threw out his challenge after pointing out that it could lead to a form of amnesty for anybody who killed more than once during the Troubles.
Rodgers, 59, was found guilty this year of murdering Eileen Doherty nearly 40 years ago.
The 19-year-old was shot three times after her taxi was hijacked by gunmen in south Belfast.
She was returning home to the west of the city from a visit to her fiancé when the killing was carried out in September 1973.
Rodgers, of Tierney Gardens, Belfast, was charged following a review of available evidence by the Historical Enquiries Team (HET). He denied the killing but was convicted on the basis of his palm prints being uncovered inside the taxi.
Once the government has set on this course it has to do it fairly. It can't pick and choose
David Scoffield QC
Although not suspected of firing the fatal shots, he was found guilty of a joint enterprise to murder.
Despite being jailed for life, he could be free after two years under the terms of the Good Friday Agreement.
Rogers, however, sought to judicially review Northern Ireland Secretary Theresa Villiers over being turned down his request for a Royal Prerogative of Mercy (RPM) request. He has already served another prison sentence for the killing of a Catholic man a year later.
Ciaran McElroy, 18, was shot a number of times in September 1974 on Park End Street, Belfast. His legal team argued that he has already served a life sentence for a Troubles-related killing carried out in Northern Ireland - putting him in a different category to former IRA gunrunner Gerry McGeough.
Dungannon man McGeough, who was jailed for the attempted murder of a part-time soldier in 1981, failed to secure an RPM because he had not served time in British or Irish jails for other offences in Germany and the United States.
In court David Scoffield QC, for Rodgers, claimed the refusal was irrational and procedurally unfair when compared to other cases where pardons were granted.
"The evidence clearly establishes that the government had this policy of supplementing the Good Friday Agreement early release scheme," he said.
During exchanges Mr Justice Treacy said: "If you were right this would amount to a de facto amnesty for anybody previously convicted of a terrorist-related offence and who had served the requisite period of time... namely two years in prison."
Mr Scoffield stressed that it would only apply to Troubles-related crimes committed before the Good Friday Agreement.
Tony McGleenan QC, for the Secretary of State, pointed out that the RPM request was made before Rodgers was convicted.
"The applicant's contention was he would never serve a minute in prison for the sectarian murder of that young girl on the Annadale Embankment in 1973," he told the court. "That, in my submission, is unconscionable."
Following submissions Mr Justice Treacy refused leave to seek a judicial review.
With reasons for his decision set to be given next week, the judge ordered that Ms Doherty's next of kin should be notified of the case.