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Giuliani: Much work left to "clean up" Mideast

The killing of al Qaeda leader Osama bin Laden brings a sense of relief and "deep satisfaction," but "we haven't won this war yet" and shouldn't consider drawing back from our decade-long wars in Iraq and Afghanistan, former New York City Mayor Rudy Giuliani said Tuesday.

Giuliani, who was praised for his steady leadership of New York in the days and months after the 9/11 attacks almost 10 years ago, spoke to "The Early Show's" Chris Wragge.

"My reaction was one of very deep satisfaction, relief that we had finally gotten him. A certain amount of [a] sense of revenge that you don't like to admit to but it's there. That this guy really deserved what he got," Giuliani said. "There's no such thing as closure because when you lose somebody you love for the rest of your life -- the gap is there. But there are things that help. And this helps."

The Killing of Osama bin Laden

But after some celebration -- and a period of heightened awareness about possible retaliation in the short term -- the U.S. needs to recommit to its wars in the Middle East, Giuliani said.

"This war is still going on. We shouldn't fool ourselves into thinking this is like V-E day or V-J day," he said. "And I don't like this talk about pulling out of Afghanistan or pulling out of Iraq. America makes this mistake a lot. People make it. You win part of it and then you walk away and it recedes. Well we've got a long way to go in Pakistan and Afghanistan to clean it up. And we should clean it up for our safety in the long term."

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Giuliani called it very troubling that bin Laden appeared to be hiding in plain sight on the outskirts of a large Pakistani city.

"This big compound, multimillion dollar estate, cars going in and out all of the time. Strange-looking people going in and out all of the time. This is a country that keeps track through its secret service and secret police," he said. "It keeps track of what the heck is going on. I have real, real problems with this."

Still, Giuliani said, bin Laden's slaying "closes a big chapter."

"Americans are proud of the president's decision, the work that President Bush did to lead up to this, the intelligence services working and then those brave SEALS that went in and did this. This is an all plus for everybody situation and I think this is the kind of thing that makes Americans feel this is the greatest country on earth. Nobody else could have done this."

Video: Inside the White House during bin Laden raid
Lara Logan: Pakistan has "explaining to do"

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