While recalling the start of his own presidency, Mr. Bush also looked forward to the challenges awaiting his successor, calling President-elect Barack Obama "a smart, engaging person" while wishing him all the best.
"This was George Bush being the son of his father, who was a very gracious person," said CBS News chief Washington correspondent Bob Schieffer.
As others have already started , Mr. Bush offered his own views - a noteworthy event for someone who hasn't "reflected very much, at least not in public," said Schieffer. (Read (Read more analysis from Peter Maer.)
Mr. Bush defended his decisions on the Iraq war, the issue that will define his presidency like no other. There have been over 4,000 U.S. deaths since the invasion and toppling of Saddam Hussein in 2003.
He said that "not finding weapons of mass destruction was a significant disappointment." The accusation that Saddam had and was pursuing weapons of mass destruction was Mr. Bush's main initial justification for going to war.
Mr. Bush admitted another miscalculation: Eager to report quick progress after U.S. troops ousted Saddam Hussein, Mr. Bush five years ago made a victory speech in front of a "Mission Accomplished" banner, a sign that turned out to be wildly optimistic.
"In the battle of Iraq, the United States and our allies have prevailed," he declared triumphantly May 1, 2003, from the deck of the USS Abraham Lincoln off the coast of San Diego.
"Clearly putting 'Mission Accomplished' on an aircraft carrier was a mistake," he said in Monday's news conference.
He also defended his decision in 2007 to send an additional 30,000 American troops to Iraq to knock down violence levels and stabilize life in the country.
"The question is, in the long run, will this democracy survive, and that's going to be a question for future presidents," he said.
Mr. Bush referred to the enormous weight Mr. Obama is about to experience, describing what it might feel like on Jan. 20 when, after taking the oath of office, he enters the Oval Office for the first time as president. "There'll be a moment when the responsibility of the president lands squarely on his shoulders," Mr. Bush said.
And he gave his view of the most urgent priority facing the incoming president: the possibility of an attack on the United States. The Sept. 11, 2001 terrorist attacks changed the country and shaped his own presidency.
"That will be the major threat," Mr. Bush said, putting the risk of another attack over the dire economic problems now facing the nation.
"I wish that I could report that's not the case, but there's still an enemy out there that would like to inflict damage on America - on Americans."
While it may have been the last time Mr. Bush takes questions from the White House Press Corps as president, it likely won't be the last time he addresses the nation. Asked about prospects for a presidential farewell address, Press Secretary Dana Perino said, "It's customary and likely," reports CBS News correspondent Peter Maer.
The last previous time the president took questions from reporters in a public setting was Dec. 14 in Baghdad, a session that hurtled to the top of the news when Iraqi journalist Muntadhar al-Zeidi threw his shoes at Bush during a question-and-answer session with Iraqi Prime Minister Nouri al-Maliki.
Among other topics President Bush discussed:
The president says he's taken "extraordinary measures" to deal with frozen credit markets, which he says is the first step toward recovery. He says a lot of the decisions he's made have been "very aggressive" ones, aimed at keeping the financial system from "cratering." And he says lending is "beginning to pick up."
Mr. Bush also says he will always defend his position that tax cuts are the "right course of action."
Looking back on his administration's record on the economy, Mr. Bush said he inherited a recession and left amid one, but that his term in office also included 52 straight months of job growth.
"Don't tell me the federal response was slow when there was 30,000 people pulled off roofs" not long after the hurricane passed over the Gulf Coast.
He said it was "a devastating storm" and that hard work remains to bring New Orleans back to the kind of life people had before the hurricane that hit in the summer of 2005.
He told the press that he disagrees "strongly" with the assessment that the U.S. has been damaged by the war in Iraq or by the way the nation has gone after terrorists.
Mr. Bush says some countries criticized the American prison for terror suspects at Guantanamo Bay, but then weren't willing to take any detainees.
And he says people who criticize the way the U.S. gets information from terror suspects are asking after the Sept. 11, 2001, attacks why officials in Washington hadn't been able to "connect the dots" ahead of time.
Mr. Bush says most of the world still sees Americans as a "strong, compassionate people" who care about freedom.
For years, Washington and Pyongyang have been locked in a standoff over Pyongyang's nuclear ambitions.
Six-nation talks aimed at resolving the dispute have been stalled due to the North's refusal to accept a protocol that would allow verification of its nuclear programs' list.
Mr. Bush said Monday in a news conference that if North Korea wants to improve relations it "must honor the commitments it made to allow for strong verification measures."
He said that it was "still a problem."
Mr. Bush said that presidents can try to avoid hard decisions and controversy, but that it's not his nature to do so. He said he's been "willing to take on hard tasks," and understands that in times of war, "people get emotional."
He said he hasn't been alone in being the target of dissent. Bush said he's been reading a lot about Abe Lincoln, who he says faced his own share of criticism.
Mr. Bush said he wishes Mr. Obama "all the very best."
The outgoing president doesn't plan to maintain a high profile. He says he's leaving the stage for good, adding that there's only one president at a time.