(CNSNews.com) - Former New York City Mayor Rudy Giuliani said he suspects that in the future, he may want to run for office again -- "but I'm not looking at anything right now."
He said he's not looking for a job right now -- in President Bush's Cabinet, say -- but he also said he wouldn't "rule things out."
In an interview with Fox News Tuesday morning -- the morning after his well-received speech to the Republican National Convention -- Giuliani said he addressed his Monday-night remarks to people who believe "the only way in which we're going to defend ourselves against terrorism is overseas."
No matter how much money President Bush spends on homeland defense, "if we don't go find them overseas, they'll find a way to attack us...We have to be on both offense and defense," Giuliani said.
He said for him, President Bush's willingness to fight terrorism is the most critical issue of the campaign.
Giuliani said he thinks President Bush has taken the United States through some of the worst times in its history; and he said it's ridiculous to suggest that President Bush should not mention the events 9/11 in the course of his campaign.
Look at all the people who are attacking Bush over his handling of the war on terror, Giuliani said; not to defend him would be wrong:
"It would be as if Abraham Lincoln would have to run for re-election in 1864 and couldn't discuss the Civil War. Of course the president has to be able to discuss why we're conducting this war. It stems from Sept. 11, 2001. And I have no doubt that there's no question that he will conduct it much more resolutely than John Kerry, who can't figure out whether he's pro-war or anti-war -- it almost depends on the day."
Giuliani said he believes there are a lot of Republicans like him -- Republicans who believe strongly in the "core" issues, which he defined as national defense, the war on terror, foreign policy, and law enforcement.
In his speech Monday night, Giuliani said neither the Republicans nor the Democrats have a monopoly on virtue. But he said there are times when leadership is the most important thing:
"And since September 11th President Bush has remained rock solid," Giuliani said. "It doesn't matter how he is demonized. It doesn't matter what the media does to ridicule him or misinterpret him or defeat him.
"They ridiculed Winston Churchill. They belittled Ronald Reagan. But like President Bush, they were optimists; leaders must be optimists. Their vision was beyond the present and set on a future of real peace and true freedom.
"Some call it stubbornness. I call it principled leadership. President Bush has the courage of his convictions.
"In choosing a president, we really don't choose a Republican or Democrat, a conservative or liberal. We choose a leader. And in times of danger, as we are now in, Americans should put leadership at the core of their decision.
"There are many qualities that make a great leader but having strong beliefs, being able to stick with them through popular and unpopular times, is the most important characteristic of a great leader.
"Winston Churchill saw the dangers of Hitler while his opponents characterized him as a warmongering gadfly.
"Ronald Reagan saw and described the Soviet Union as "the evil empire" while world opinion accepted it as inevitable and belittled Ronald Reagan's intelligence.
"President Bush sees world terrorism for the evil that it is. John Kerry has no such clear, precise and consistent vision. This is not a personal criticism of John Kerry. I respect him for his service to our nation.
"But it is important to see the contrast in approach between the two men; President Bush, a leader who is willing to stick with difficult decisions even as public opinion shifts, and John Kerry, whose record in elected office suggests a man who changes his position often even on important issues. "
Giuliani said no matter what happens on Election Day, "President George W. Bush already has earned a place in our history as a great American president."