Speaking after a meeting the Nobel Peace Prize laureate in Rangoon yesterday, Mr Cameron said a visit in June would enable the 66-year-old politician to return to her "beloved Oxford", where she took a degree in the late 1960s and where she met her late husband, the academic Michael Aris, who died in 1999.
Ms Suu Kyi, who has spent 15 years under house arrest by the country's military junta, did not quite commit herself to accepting the invitation, saying: "Two years ago, I would have said thank you for the invitation but sorry. Now I am able to say – perhaps. That is great progress."
For many years, the pro- democracy leader has lived under the threat that if she ever left her homeland, she would not be allowed back.
Burma, a British colony until 1948, has been ruled for almost half a century by a military junta, which has wielded absolute power and stifled almost all dissent. The EU, US and other nations have imposed trade and other sanctions.
However, last year the installation of a military-backed, nominally civilian government, which has introduced a series of reforms, including the release of hundreds of political prisoners, has led to speculation that decades of international isolation could be coming to an end.
During his historic visit – the first of any UK premier for 60 years – Mr Cameron said: "It is right to suspend the sanctions that are against Burma – to suspend them, not to lift them and obviously not to include the arms embargo – because it's important to send a signal that we want to help see the changes that can bring the growth of freedom and human rights."
Standing beside Ms Suu Kyi at a joint press conference in the garden of her lakeside villa, the PM, who had earlier met Burmese President Thien Sein in the capital Nay Pyi Taw, added: "Burma shouldn't be as poor as it is, it shouldn't have suffered under dictatorship for as long as it has, and things don't have to be that way.
"There is the real prospect of change and I'm very much committed to working with you in trying to help make sure that your country makes those changes."
Mr Cameron stressed that the West had to be cautious, needing to know the reform process was irreversible. "All courses of action are full of risk but this is the right step. We are not starry-eyed or credulous about this. We know what a long, hard road needs to be travelled between now and 2015," he added.
In two weeks' time, EU foreign ministers will discuss policy towards Burma; sanctions are due to expire on April 30 unless they choose to renew them.
Ms Suu Kyi made it clear she supported the suspension of the sanctions as this would acknowledge the changes the president and his colleagues had begun.
She described it as a "calculated risk".
However, she also stressed: "It would also make it quite clear to those who are against reform that should they try to obstruct the way of the reformers, then sanctions could come back."
The Burmese opposition leader, whose party won 43 of the 45 recent parliamentary by-elections, paid tribute to the "help friends have given us over these last decades, especially Britain".
She added: "They have always understood our need for democracy, our desire to take our place in the world and the aspirations of our people."