Cameron also met Burma's reformist President Thein Sein as he became the first Western leader in decades to visit the country, which languished for decades under a repressive junta until military rule ended last year.
The British premier announced a dramatic shift in stance following Suu Kyi's recent election to parliament, calling for all European Union measures except the arms embargo to be suspended, but not scrapped completely.
"If we really want to see the chance of greater freedom and democracy in Burma, we should respond when they take action," Cameron said in the grounds of Suu Kyi's lakeside home where she was locked up for much of the past 22 years.
"For the sake of a country that has been crying out for freedom after decades of dictatorship, and that is crying out for a stronger economy after so much grinding poverty, it must be worth taking that risk."
Britain -- Burma's former colonial ruler -- has traditionally taken a hardline stance on sanctions because of human rights concerns and its shift is likely to clear the way for a suspension of the measures later this month.
The 27-nation European Union already lifted some restrictions against the regime this year and foreign ministers will decide the next steps when they meet on April 23.
Suu Kyi, a Nobel Peace Prize laureate whose support is seen as crucial for any easing of European and US sanctions, for the first time also called for a suspension of the measures against her country.
"This would strengthen the hands of the reformers -- not just the suspension but the fact that there is always a possibility of sanctions coming back again if the reforms are not allowed to proceed smoothly," she said.
"We still have a long way to go but we believe that we can get there. I believe that Thein Sein is genuine about democratic reforms."
Earlier Friday Cameron held about 40 minutes of talks, followed by lunch, with the president in the showpiece capital Naypyidaw.
The former general hailed the summit as "historic" as he welcomed Cameron to his official residence.
"We are very pleased and encouraged by your acknowledgement of Burma's efforts to promote democracy and human rights," he said.
A steady stream of foreign dignitaries, including US Secretary of State Hillary Clinton and British Foreign Secretary William Hague, have visited Burma since a new quasi-civilian government took power last year.
But Cameron is the first Western head of government to go there since the military seized power in 1962, ushering in almost half a century of repressive junta rule and isolation from the West.
He is believed to be the first serving British prime minister to visit Burma, which won independence in 1948.
Cameron said that despite the progress by the new government, more needed to be done, including the release of remaining political prisoners and finding a political solution to ethnic conflicts.
He lauded Suu Kyi as an "inspiration" and invited her to visit Britain in June -- an offer she said she could "perhaps" now consider given receding fears that she would not be allowed by the authorities to return home.
Foreign ministers from the Group of Eight world powers -- Britain, Canada, France, Germany, Italy, Japan, Russia and the United States -- on Thursday welcomed "significant steps" by Burma toward democratic reform.
"The ministers will consider the easing of sanctions to help this country embed reform and fully integrate into international and regional political and economic processes," they said in a final statement after talks in Washington.
In February, the European Union lifted a travel ban on 87 Burma officials, including Thein Sein, but kept an assets freeze against them.
Other EU sanctions include an arms embargo, a ban on gems and an assets freeze on nearly 500 people and 900 entities.
