However, he defended his administration's record on the Middle East, saying he felt he had "advanced the process" despite the widely perceived failure of the Annapolis talks in 2007.
Bush also used his final news conference to insist he remained "for a sustainable ceasefire" in Gaza, but said Hamas must stop firing rockets into southern Israel.
Also on Monday, Bush agreed to Obama's request for congress to release the remaining $350bn of the $700bn bailout for the country's financial sector.
The request gives Obama the ability to access the money and also change the programme's aims and conditions.
The Bush administration was strongly criticised by congress and financial watchdogs for the handling of the first $350 billion of the bailout.
Bush, whose popularity reached record lows in his second term, also defended his decision in 2007 to send an additional 30,000 US troops to Iraq in a bid to combat fighters opposed to the government and the US military presence.
"I strongly disagree with the assessment of our moral standing has been damaged - people still understand America stands for freedom"
"The question is, in the long run, will this democracy survive [in Iraq], and that's going to be a question for future presidents,'' he said.
He also said the most imminent challenge Obama would face was the prospect of another attack on the US.
"I wish that I could report that [this is] not the case, but there's still an enemy out there that would like to inflict damage on America - on Americans," he said.
He also described North Korea and Iran as "still dangerous," saying Pyongyang may be enriching uranium for possible nuclear weapons.
'Standing for freedom'
On domestic issues, Bush defended the government's response to Hurricane Katrina in 2005, which decimated the city of New Orleans and parts of the US's Gulf Coast.
|Bush said he remained 'for a sustainable
ceasefire' in Gaza [AFP]
"Don't tell me the federal response was slow when there were 30,000 people pulled off roofs right after the storm passed," he said.
"Could things been done better? Absolutely. But when I hear people say the federal response was slow, what are they going to say to those chopper drivers or the 30,000 who got pulled off the roof?"
And he grew irritated when asked if the US's moral standing in the world had suffered as a result of his presidency.
"I strongly disagree with the assessment of our moral standing has been damaged. People still understand America stands for freedom," he said.
He said that keeping the US safe had been more important to him than personal popularity.
"I would not worry about popularity. What I would worry about is the constitution of the United States and putting plans in place that make it easier to [find out what] the enemy is thinking."