In an interview for the Breakfast With Frost programme - to be broadcast on BBC One on Sunday morning - Mr Bush Senior said the current crisis was very different to the Gulf War in which he headed the international coalition to expel Iraqi forces from Kuwait.
"It's not going to be a 100-hour ground war, or a very effective TV air war - it's going to be a different kind of a battle to win, but there's a determination, amongst world leaders, that we will win," he said.
'Enemy more shadowy'
The "First Father" is taking a back seat as his son leads a campaign against those responsible for the devastating suicide hijack attacks against the US on 11 September.
But he told the BBC about the differences between the 1991 and 2001 campaigns, and his son's handling of the crisis so far.
"What's different about it is in the Gulf War we could see what the enemy had done... we knew where his forces were and we knew we had to mobilise public opinion [and] press support.
"We had to go to the United Nations to get resolutions passed and then we had to go to battle and what Saddam had said would be the 'Mother of all Battles'," the former president said.
"But in this case public opinion is for the president and Tony Blair and others... but the enemy is much more shadowy, much more difficult to pin down and Osama Bin Laden seems to be the most evil of evil but there are a lot of other people in this network."
Special relations
Mr Bush also spoke in glowing terms about the so-called "special relationship" between Washington and London, which was "strong and intact", and was embodied by the "touching" sight of seeing Mr Blair "in the gallery sitting with our Laura" during George W Bush's address to the nation last week.
When asked about whether he felt that a Middle East peace settlement was now more urgent because of the benefit that would have in eradicating terrorism, Mr Bush had this to say:
"So I think it makes it much more urgent that we find a way - somebody, the political people in our county, in your country, around the world - to get a settlement," he said.
'Moral' campaign
In 1991, President Bush appeared on the same BBC programme and told David Frost that "nothing of this moral importance since World War II has faced the nation".
Did he see the threat now posed by international terrorism of equal "moral importance"?
"There the integrity of a member of state of the Union of the United Nations [Kuwait] was threatened, indeed the nation would have been obliterated if we all hadn't come together in coalition and done something about it.
"But I think in terms of moral importance, I think what's happened is so offensive that world opinion will recognise this as a landmark and will stay supportive of the United Kingdom, of the United States and other countries that are determined to do something about it."
Nevertheless he was conscious of the "sensitivities" of the 2001 operation - and acknowledged the possibility of losing of crucial Arab and Muslim support - though that was an issue the US had to face in 1991.
Mr Bush said that his son was "very sensitive" to Nelson Mandela's warning that Washington "must avoid any course of action which will be as unpopular as that of the terrorists".