The request for recusal was made by the Sierra Club, an environmental group that alleged that it was improper for Scalia to take a January duck-hunting trip with Cheney while the high court was considering an appeal involving a request for the release of information about Cheney's energy task force.
In an unusual 21-page memorandum, Scalia closely analyzed his relationship with Cheney, the particulars of the hunting trip, as well as the high court's history of friendly social relations with administration officials.
"A rule that required members of this court to remove themselves from cases in which the official actions of friends were at issue would be utterly disabling," Scalia wrote.
Many Supreme Court justices get their jobs "precisely because they were friends of the incumbent president or other senior officials," he wrote.
The Supreme Court decided in mid-December that it would review Cheney's appeal to keep his energy task force papers secret.
The Sierra Club and another group, Judicial Watch, are pressing for the documents. They sued in 2001 to find out the names and positions of members of the energy task force, which was headed by Cheney that year.
The Sierra Club asked for Scalia's recusal in February, pointing to the "American public's great concern about the continuing damage this affair is doing to the prestige and credibility of this court."
Scalia said that the hunting party had nothing to do with the impending case.
"The vice president and I were never in the same blind and never discussed the case," Scalia said, referring to a shelter used to conceal duck hunters.
"Nor was I alone with him at any time during the trip, except, perhaps for instances so brief and unintentional that I would not recall them -- walking to or from a boat, perhaps, or going to or from dinner," Scalia said.
"Of course, we said not a word about the present case," Scalia said.
Toward the end of the memo, Scalia looked at the basic question of whether he could impartially decide the energy task force case because he "went hunting with that friend (Cheney) and accepted an invitation to fly there with him on a government plane."
"If it is reasonable to think that a Supreme Court justice can be bought so cheap, the nation is in deeper trouble than I had imagined," Scalia wrote.
"Since I do not believe my impartiality can reasonably be questioned, I do not think it would be proper for me to recuse," he said.
Several newspaper editorials have called on Scalia to remove himself from the case, something he also addressed at length in his memo.
"My recusal would also encourage so-called investigative journalists to suggest improprieties, and demand recusals, for other inappropriate (and increasingly silly) reasons," wrote the justice.
Scalia also noted in his memo that he has decided to step aside in another case this term -- one testing the constitutionality of the Pledge of Allegiance in public schools. The decision came after he criticized the lower court ruling during a speech at a religious rally.
For its part, the court itself referred to Scalia's judgement in determining whether he was able to evaluate the case fairly.
"In accordance with its historic practice the court refers the motion to recuse in this case to Justice Scalia," the court said in March.
Some Democratic lawmakers also weighed in on the issue, including Sen. Patrick Leahy, D-Vt., and Sen. Joesph Leiberman, D-Conn., who wrote a letter to Chief Justice William Rehnquist in January voicing concern about Scalia's trip with Cheney and the recusal procedure.
"A justice must examine the question of recusal on his own even without a motion, and any party to a case may file a motion to recuse," Rehnquist wrote in reply to Leahy. "And anyone at all is free to criticize the action of a justice -- as to recusal or as to the merits -- after the case has been decided."
"But I think that any suggestion by you or Senator Lieberman as to why a justice should recuse himself in a pending case is ill considered," Rehnquist added.
The Supreme Court arguments in the case are scheduled for April 27.