Bob Ainsworth said seeing that advances in Iraq's society, economy and security will persuade families that "the loss of their sons was not in vain."
British forces will start their final withdrawal from Iraq next month, six years after the invasion that toppled Saddam Hussein and cost the lives of 178 British servicemen.
In an interview with the Daily Telegraph in Iraq, Mr Ainsworth said that in future years, veterans of the British mission and their families will want to visit the country in the same way that Second World War veterans visit the Normandy beaches and other battle sites.
Hailing "dramatic" improvements in the security situation in Basra, Mr Ainsworth also accused opponents of the original invasion for taking a "jaundiced" view of Iraq today and refusing to admit that the country is now making progress.
Iraq's local elections last month passed off without significant violence and British commanders say they will leave confident that the country is on course for stability. Maj Gen Andy Salmon, the senior British officer in Iraq, last week told the Daily Telegraph that Basra is now safer than Manchester.
During his visit to Iraq, Mr Ainsworth was able to walk the streets of Basra, meeting locals and visiting businesses.
Speaking afterwards, he looked forward to the next phase in Britain's relationship with Iraq, forecasting close ties between the two nations because of their "combined history".
"There are going to be a lot of Brits who are going to feel close to this place because they have had experiences here, some good some bad," he said.
"There are going to be people who have lost loved ones here who are going to want to visit. They are going to want to understand Iraq, to see Iraq going forward. They are going to want to think that the loss of their sons was not in vain."
As the security situation improves still further, families and veterans will visit, he said. "There is still going to be an attachment to place."
He added: "As we see with Second World War veterans wanting to visit the D-Day landing sites to see where they were involved and their families wanting to do the same. The same thing is going to happen out here and of course we are going to wind up facilitating that."
Some British soldiers and diplomats in Iraq are frustrated at what they see as the British public's failure to appreciate the significant advances the country has made in recent months.
Mr Ainsworth said that some critics of the 2003 invasion - including Labour MPs - are refusing to admit that life in Iraq is getting better.
"It is difficult when you have been so opposed to the operation in the first place it is very difficult to look at with anything other than jaundiced view from then on," he said. "Some people just think Iraq must be an awful place and they can't see beyond that."
The Government is urging British companies to consider investing in Iraq, but Mr Ainsworth said that outdated fears about security were deterring many firms.
"I think people are blind to the progress to the progress that has been made," he said. "Most people, business people included, have not caught up with the reality."
Mr Ainsworth accepted that some opponents of the war would see any attempt to boost investment as an attempt to "cash in" on the conflict, or even proof that the war was in fact launched to get access to Iraqi oil.
He strongly rejected that argument but added that having lost lives and spent billions of pounds in Iraq, "it would be perverse if we do not seek to develop a good bilateral relationship with Iraq, and of course there is a commercial aspect to that."
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