Ahead of the ruling by Attorney-General John Ashcroft, McVeigh told reporters that if the relatives' request was agreed to, he would "throw it back in their face".
The killer, however, insists the entire nation has the right to witness his final moments.
Ahead of the ruling by Attorney-General John Ashcroft, McVeigh told reporters that if the relatives' request was agreed to, he would "throw it back in their face".
"I'm going to demand they televise it nationally," he said.
But the government has been keen to minimise McVeigh's ability to use a televised execution as a public forum.
Media outlets are already clamouring to conduct the final interviews with the controversial figure who carried out the single deadliest peacetime attack on US soil.
He was convicted six years ago of blowing up a government building and killing 168 people - including 19 children. He recently whipped up a storm by boasting about the crime and dismissing the children's deaths as "collateral damage".
He has implied that the bomb was in retaliation for the government's assault on a religious extremist compound near Waco, Texas.
McVeigh has long argued that since the government claimed his victims were not just the dead but America itself, then they should be allowed to witness his punishment.
Hence his demands to have it televised. He envisages the execution as "a deluxe suicide-by-cop package" - one that is worthy of being aired on the popular US news and current affairs programme, 60 Minutes.
There are reports that he has already planned his final words.
He is expected to recite from the famous 19th-century poem Invictus by William Ernest Henley:
"I am the master of my fate:
I am the captain of my soul."
Contingency plans
But the event is being carefully stage managed by the prison authorities, too.
This is certain to be a very public affair and officials have been drawing up contingency plans to ensure nothing goes wrong.
The death penalty is an issue that provokes surprisingly little public debate in the US - unless it is a celebrated murderer or someone who has been wrongly convicted.
But prison officials in the tiny Indianan town of Terre Haute are bracing themselves for an onslaught from survivors and victims' relatives, pro- and anti-death penalty protesters, plus nearly 1,500 journalists.
Preparations for the media circus are already under way, including eliciting the services of a local firm used to corporate hospitality catering.
Hostage threat
For a little more than $1,000 reporters can work in luxury tents and be ferried around beautiful grounds less than a mile from the prison in golf carts.
This is the federal government's first execution for 37 years and, consequently, prison officials felt the need to draw up a 54-page execution protocol.
The confidential plan, which was leaked to the Los Angeles Times, calls for the creation of a command centre at the prison and law enforcement teams to control protesters if they become unruly.
Officials are expected to bus in demonstrators and limit their personal belongings to a few items, such as a Bible and a candle. This is to avoid a repetition of the 1989 execution of serial killer Ted Bundy, where groups carried mock electric chairs and waved frying pans
The document also refers specifically to the threat of disturbances by prisoners in the jail and the possible taking of hostages.
It also specifies the execution be carried out in a "humane manner".
McVeigh will be strapped down and covered neck to feet in a sheet.
Next, curtains to the gallery will be pulled back and 30 witnesses and a senior official will declare themselves ready.
The condemned man will then be given an injection of sodium pentothal, which will render him unconscious. Next pancuronium bromide, which will collapse his lungs.
And finally, potassium chloride, which will stop his heart from beating.