Bush, accused by Democrats of using Sunday's warning of potential threats to financial institutions in New York and Washington to divert attention from White House rival John Kerry, said it was important to share "real" intelligence.
"When we find out intelligence that is real, that threatens people, I believe we have an obligation as government to share that with people," Bush told a conference of minority journalists.
"Imagine what happens if we didn't share that information with the people in those buildings and something were to happen?"
He added: "This is a dangerous time. I wish it wasn't this way. Now, I wish I wasn't the war president. Who in the heck wants to be a war president?"
Bush later challenged Kerry to say straight out if he would have supported the 2003 invasion of Iraq if only to eliminate the danger that Saddam Hussein could have developed weapons of mass destruction.
No weapons found
"Even though we did not find the stockpiles that we thought we would find, we did the right thing. He had the capability, and he could have passed that capability on to our enemies," Bush said at a campaign picnic rally in New Hampshire.
"Now, there are some questions that a commander-in-chief needs to answer with a clear yes or no. My opponent hasn't answered the question of whether knowing what we know now, he would have supported going into Iraq," he added.
"I have given my answer. We did the right thing, and the world is better off for it."
A Kerry campaign aide, responding to the president's remarks, said the Democratic nominee had previously made clear "it was right to hold Saddam Hussein accountable and we're glad he's gone".
"But the way President Bush took the country to war was wrong," said Kerry Senior Adviser for National Security Affairs Susan Rice. "[He] rushed into war without our allies, without a plan to win the peace, and without properly equipping our troops."
Journalists attending the Unity conference in Washington gave Kerry loud applause when he appeared before them on Thursday, so Bush had little doubt about the group's political leanings when he agreed to talk to them.