The Foreign Office sought to identify countries that could pose "similar risks" as Afghanistan, a senior former diplomat told the Iraq Inquiry.
Stephen Pattison said the phrase was dropped after it emerged it had been taken from a magazine article.
Mr Pattison told the inquiry the process led to Iraq moving up the political agenda after 9/11.
Mr Pattison, who oversaw the Foreign Office's dealings with the United Nations in the run-up to the 2003 invasion said: "After 9/11, there was obviously considerable concern about areas of the world which might pose a threat.
"There was a phrase that was current at that time which was 'draining the swamp'.
"It was the title of a paper put up by our planning department about how we could address areas of the world which post 9/11 might fit into the same pattern - areas like Afghanistan - which frankly we had not paid enough attention to before 9/11 and which had resulted in an attack on the US.
"The 'draining the swamp' line was a bit about: 'let's look around and see where there might be other places that could pose similar risks'."
Although the phrase "encapsulated" the post 9/11 security approach, he said it was soon dropped "partly because I think it actually came from a published magazine article".
Panel member Sir Roderic Lyne, a former Ambassador to Russia, asked him whether the phrase "didn't originally come from Chairman Mao".
He replied: "I think it originally did but then I think it was taken up by the Economist in the context of the post 9/11 stance. The thought behind it, I think, was the thought which drove the then British government into focusing very hard on Iraq."
The phrase "draining the swamp" is commonly attributed to Chairman Mao - but Dr Yiyi Lu, a Chinese expert at Chatham House, said she did not immediately recognise the phrase and that its meaning seemed "too vague".
Asked about the decision to go to war, Mr Pattison said the UK was driven by rather "idealistic" motives rather than direct concerns about its own security or a decision to alter the balance of power in the region.
"I think Tony Blair's view was always that - the idealists' view that we were doing this to make the world a safer place. We were not doing this because there was a direct threat to the UK; we were doing this because it was in the interests of the international community and because it was in the interests of the international community he expected the international community to step up to the plate and do it."
The Iraq Inquiry is concluding its latest round of hearings - expected to be the last before it starts the process of compiling its report.
Former foreign secretary Jack Straw will give evidence for the third time on Wednesday.

The NCS aims to prepare teenagers for work through team building activities and community projects.
It has run in England since 2011 and a pilot scheme began in Wales in 2014.
Mr Cameron, visiting Snowdonia, said it was a "fantastic opportunity" for young people.
The intention is that graduates on the scheme, called Teach First, lead teenagers on group activities and challenges like mountaineering, canoeing and abseiling.
More than 1,700 graduates joined Teach First in England and Wales this year, and the intention is for all to be involved in the volunteer scheme by 2017.
Visiting an outdoor education centre in the Conwy valley on Friday, Mr Cameron said: "NCS is a fantastic opportunity for young people from different backgrounds to come together to gain life skills and give something back to their local community.
"Teach First's mission to break down social barriers makes its teachers ideal volunteer mentors to engage with and inspire young people on NCS.
"This fantastic partnership will create thousands more opportunities for young people to benefit from NCS."
The NCS is a key part of Mr Cameron's "Big Society" agenda, encouraging the growth of volunteering and promoting so-called social enterprises.
The prime minister urged the Welsh government to consider taking up the scheme and offering it across Wales.
A report on the Welsh pilot - examining whether it duplicates or complements existing schemes - is expected shortly.
The UK government has been embroiled in controversy this week after one high-profile charity, Kids Company, closed its doors after ministers said they wanted to recover a Â£3m grant.
There have been suggestions that Mr Cameron himself had been "mesmerised" by the charity's founder Camila Batmanghelidjh, and had over-ruled civil service concerns over continued funding for the organisation.
The UK drew up a list of countries seen as potential threats after 9/11 in a process known as "draining the swamp".
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Graduates who do a two-year teaching scheme will be expected to volunteer with the National Citizen Service (NCS), Prime Minister David Cameron has announced.