From January 2007 to September 2008 General Petraeus served as Commanding General, Multi-National Force - Iraq, and now, as Commander of US Central Command, he is responsible for US operations in Afghanistan.
Speaking this week to The Sun newspaper, General Petraeus praised British troops saying:
"I have always been impressed by the courage, capacity for independent action, skill and exceptional will of your soldiers.
"It's what sets forces in the UK and I'd argue the US and a handful of other countries apart from all others in the world."
Regarding the British forces deployed to Afghanistan he said:
"British troops have been in a very tough place and they have done exceedingly well.
"It is enormously important we achieve our objective in Afghanistan, and ensure it does not again become a sanctuary for Al Qaeda and other extremists that have carried out attacks on your streets.
"There has been progress in Helmand province. Expanding the security bubble for example has allowed people to vote who would not have had that opportunity a few months ago."
Addressing the British public he added:
"I want to thank the British public because regardless [of] what they've felt about these endeavours they've always supported our troops and their families. They have recognised the sacrifices they have made."
Speaking to Sky News this week General Petraeus reiterated why British and other coalition troops are fighting in Afghanistan. He said:
"This war is all about ensuring that Afghanistan does not once again become a sanctuary for Al Qaeda and trans-national extremists, as it was under the Taliban in the past, who carried out attacks in 9 /11 and London and other locations in the United Kingdom and other western European countries and the rest of the world.
"That is a hugely important interest, those organisations, those extremist elements do not want us to enjoy the freedoms that we've fought for for centuries and it is again very important that they not have safe havens in which they can train and plan such attacks around the world."
When asked whether deploying coalition forces to Afghanistan antagonised feelings towards the US and the UK, General Petraeus said:
"Well I think that depends on how you act and if you are truly seen to be there for the people to improve their security, to help make their lives better, then, indeed, you gain popular support.
"But that's the key element and the people are not tolerant of foreigners who are there who are not improving their security. They are supportive of those who are in fact taking steps to improve their lot in life."
Speaking about yesterday's elections in Afghanistan the General said:
"Ambassador Holbrooke provided a report that said that the Taliban did not disrupt the election. Again turnout was reported to be low in the morning but did build during the day so I think it would be premature to try to characterise it overall or to try to slice and dice this just yet.
"But the fact is, again as the Ambassador said, the election went forward, it was not disrupted, there were certainly acts of violence around the country, certainly places where polls were not able to open for a variety of reasons. But the vast majority of them did, as I noted earlier I think some fifty-two or sixty-two hundred out of about sixty-five hundred that were planned actually did have [the] election going on."
Describing what victory in Afghanistan means, General Petraeus said:
"Victory looks like a gradual hand-off of tasks to Afghan security forces, Afghan Government elements over time. Frankly it is the same as what took place in Iraq, it's the same that has taken place in other cases in your history and in ours, but even more so in yours."