Rejecting the notion that he called the shots and thus pulled the strings for President George W. Bush, former Vice President Dick Cheney defended the Iraq War, saying it was the president's decision to invade and go after Saddam Hussein in 2003.

I think the president made the decision, Cheney told NBC's Matt Lauer. He felt strongly about it, too. He understood the dimensions of what we were doing. I certainly supported it. I advocated it. I thought it was the right policy. I believe that still today.

Cheney, whose memoir In My Time hits bookstores Tuesday, disputed the notion that the decision to invade Iraq weakened America's standing in the global community, NBC reported.

Cheney: U.S.'s Standing Not Damaged By Iraq War

I just don't think that it damaged our reputation around the world, Cheney said. I just don't believe that. I think the critics at home want to argue that. In fact, I think it was sound policy that dealt with a very serious problem and eliminated Saddam Hussein from the kind of problem he presented before.

What would've happened this week if Moammar Gadhafi had still been in power with a nuclear weapon in Libya? Would have fled? I doubt it.

Cheney also talked about the conflicting accounts in his book, compared to Bush's, saying the two did not collaborate or discuss the contents of his book before it went to press.

I did not cooperate or coordinate on our book, Cheney said. He wrote his book, I wrote my book. If they were identical in their treatment of these events, people would say, 'Looks like plagiarism to us,' or 'They cooperated. It's a conspiracy of some kind.' In fact what it was, was a serious effort by me to put down the events that I remember. I'm sure the president did the same.

Bush's account has the president dismissing his advisors when making the ultimate decision to invade Iraq in the aftermath of Sept. 11. In his book, Cheney maintains that Bush, after dismissing the rest of his advisors, asked him what to do privately.

I can't make that case, Cheney said when asked whether he ultimately pushed Bush into war with Iraq. We needed to take the action we did.

Cheney's Proudest Accomplishment: Preventing a Second Terrorist Attack

If you look back at the proposition that we faced after 9/11 with respect to Saddam Hussein, we were concerned with the prospects of terrorists like the 9/11 crowd acquiring weapons of mass destruction. I think that's the biggest threat we face. At the time, to go after Saddam Hussein and take him down, we eliminated a major source of proliferation.

And preventing another terrorist attack is what marks his proudest moment as vice president.

The most important thing we did after 9/11: We prevented all further mass casualty attacks on the United States, he said.