This is a rush transcript from "On the Record," June 12, 2012. This copy may not be in its final form and may be updated.

GRETA VAN SUSTEREN, FOX NEWS HOST: Senator John McCain warning the Obama administration that it cannot police itself. He is calling for special outside counsel to investigate the leaks of highly classified information. Attorney General Eric Holder has appointed two U.S. attorneys, one appointed by former President Bush, to look into recent national security leaks. But Senator McCain says that is not good enough.

(BEGIN VIDEOTAPE)

VAN SUSTEREN: Senator, nice to see you, sir.

SEN. JOHN MCCAIN, R-ARIZ.: Thank you.

VAN SUSTEREN: All right, you have asked or you want a special prosecutor, independent of what the attorney general has done, to investigate the leaks. Why?

MCCAIN: Well, first of all, it's a special counsel, to be specific. But we need an outside investigation. Clearly, the attorney general of the United States is under considerable criticism and scrutiny. Over in the House, they are talking about citing him for contempt of Congress.

But more importantly than that, we need someone who is completely independent. We did that in various other occasions which were far more serious than this, the Valerie Plame investigation and others.

When the Democrats, Abramoff and others, we've got letters from then- Senator Obama and statements by vice president -- then-Senator Obama calling for an independent counsel or special investigation.

So it's clear that this issue is of transcendent importance. The director of national intelligence said this is the most egregious breach of security and national security that he's seen in his 30 years as a -- in the intelligence community.

VAN SUSTEREN: Well, it's bipartisan in the sense that there is horror or shock on both sides of the aisle. Senator Dianne Feinstein, Democrat, very concerned about the seriousness of these leaks.

Let me -- let me ask you, though, is that two people were appointed by Attorney General Holder. One was the United States -- was a U.S. attorney appointed by President Obama. The other one is a U.S. attorney out of the District of Maryland, appointed by then-President Bush. Does sort of the bipartisan nature of that or their background in any way relieve any of your thoughts?

MCCAIN: They still have to report to the attorney general of the United States. They are not independent. It requires an independent look at this in order to have the kind of credibility that's necessary.

Look, this is the most egregious breach of national security that I have ever seen. We are talking about ongoing highest-level covert operations, one on cyber-warfare and the other on drones. And this requires, then, the most objective and credible investigation, someone like Bob Bennett. We would all applaud -- as you remember him, he's done other investigations. And he's a Democrat, as a matter of fact. But we need someone who's credible and someone who's truly independent.

VAN SUSTEREN: How about speed, though? I mean, we get sort of -- we get into these huge investigations. They go on for years and years and become almost sort of a Shakespearean play developing here in Washington, where people are pointing fingers. I mean, one of the things is that we need a swift decision. Does going outside also, though, run the risk that it'd be being greater time, or not?

MCCAIN: Do you think that if Attorney General Holder was ultimately in charge of this investigation that we would have any information between now and November? The fact is that a special counsel would be constrained, in some degrees, whereas a, quote, "independent" counsel, which we -- that law has lapsed, would have much more constrained jurisdiction.

And I'm confident that we would get the best possible conclusion, a credible one that the American people could say, Well, that was independent, and so therefore, we trust it.

VAN SUSTEREN: Well, it's sort of oddly -- and I think we can get to it -- is that the small universe of people at some of these meetings ought to make it rather swift that you could find out who is the leaker. I mean, it's not as though there's a huge universe of people who were present in the room when this national security information was discussed. So it actually -- it could be done efficiently and quickly, whoever does it.

MCCAIN: Well, I hope so. But the author of the book and the other publication clearly indicate that this goes to -- to the administration, and in some cases, the highest levels of the administration. I don't think there's any doubt about that.

So it's -- it really is awful. You know, the anecdote that the -- after the information was disclosed about the Usama bin Laden, including SEAL team 6, including other information -- the secretary of defense, probably the most respected of all cabinet members -- as you know, he was appointed under President Bush, Secretary Gates -- went to the White House and said to the national security adviser, Mr. Donilon, he said, I've got a new communication strategy for you. Donilon said, What is it? He said, Shut the "f" up.

Now, that is a very unusual move for a secretary of defense to tell the national security adviser. That's how concerned the secretary of defense was at that time about the raid conducted on Usama bin Laden. And now we have additional disclosures of the most covert operations.

And by the way, our relations with the Israelis and other nations has been severely damaged by these revelations.

VAN SUSTEREN: Two issues. One is whether or not it was leaked for political reasons. I'll get to it in a second. But the other is the actual leaks and how damaging to our national security. And one of the articles, David Sanger of The New York Times talks about this cyber-worm, the Stuxnet, which was supposed to infiltrate the Iranian nuclear computer system for their nuclear power plant and then disrupt it and thereby...

MCCAIN: And it did.

VAN SUSTEREN: And it did.

MCCAIN: And it did.

VAN SUSTEREN: It did. But here's what -- here's what's interesting that he wrote. He says, "At a tense meeting in the White House Situation Room within days of the worm's escape, Mr. Obama, Vice President Joe R. Biden, Jr., and the director of the Central Intelligence Agency at the time, Leon Panetta, considered whether America's most ambitious attempt to slow the progress of Iran's nuclear efforts had been fatally compromised."

Now, there's a universe of people who were in the room there. You would expect some of their aides, as well?

MCCAIN: I would think that there would be others, including the national security adviser, in the room, I would assume. But that's something we need to find out because those are direct quotes, as you know, from what actually happened.

VAN SUSTEREN: In fact, the next paragraph has the quote, President Obama asking, "Should we shut this thing down?" Meaning what the president is talking about, about a national security matter, is now in the public domain in The New York Times.

MCCAIN: All I can say is that every indication leads to the conclusion, or the substantive substance to the belief that this leaks came from the highest levels. That's all I can assume.

But I am not saying that that is the case. That's why we need the investigation. But also, you know, whenever there's leaks in this town -- and you've seen this before -- the first question you ask yourself and should be asked in the case of leaks -- who benefits?

VAN SUSTEREN: Or is somebody stupid? I mean, there's also the stupid factor.

MCCAIN: Yes. Yes.

VAN SUSTEREN: Did someone go and tell somebody else who told somebody else who told somebody else. I mean, who doesn't get what national security and classified means?

MCCAIN: Yes. Who benefits. But in response to what you just said, in his book, Mr. Sanger said several officials said that they wanted to remain anonymous because they would lose their jobs. So I think it's -- it's pretty clear here.

VAN SUSTEREN: Well, in fact, in the Sanger article in The Times, it said none would allow his names to be used because the effort remains highly classified and part of it continues to this day. So the source knew it was wrong to be talking about it because the source didn't want his name out.

MCCAIN: Highly classified, going on to this day. One of the reasons why this is so egregious is these operations were going on, and as far as I know, obviously, they're still going on. And so lives have been compromised. National security has been compromised.

And what has been the result? An estrangement between ourselves and our allies, compromised of our most highly classified operations, and now we have told the enemy what we are doing. And over time, don't they feel then a license to respond?