Cameron met Friday with Myanmar opposition leader Aung San Suu Kyi, who secured a seat in the country's Parliament in recent elections following her 2010 release from house arrest.
Suu Kyi spent several years under house arrest after the former ruling junta failed to recognize a 1990s victory for her National League for Democracy Party.
Cameron said at the home of the Nobel Peace Prize laureate that suspending sanctions against Myanmar would be a "bold move"
"I think it is right to take this first step," he was quoted by Bloomberg News as saying.
Suu Kyi said easing sanctions would "strengthen the hand of reformers" in a country ruled by military leaders for many years.
Myanmar has earned praise from the international community for taking steps toward democracy. Human rights, however, remain in a concern for the country formerly known as Burma.
Cameron's visit was the first by a British leader since the country gained independence from the United Kingdom in 1948.