On the first visit by a UK foreign secretary to Burma for 55 years, he said that releasing all detainees would be the price for lifting sanctions.
His counterpart Wunna Maung Lwi promised that changes in Burma were "irreversible". But he later said Burma did not acknowledge there were political prisoners.
Mr Hague said: "My message is, if you want those sanctions - those restrictive measures as we call them - lifted, then it is very important to show that you are completing this process of reform. "We believe now that you are sincere about it, so now get ahead quickly and complete it by releasing the remaining political prisoners and by showing that the upcoming elections are free and fair."
Mr Hague made the comments after meeting his counterpart in Nay Pyi Taw. "The foreign minister has reaffirmed commitments that have been made to release political prisoners," he told reporters. "I stressed that the world will judge the government by its actions."
But in an interview with the BBC Burmese service later, Wunna Maung Lwi said Burma did not acknowledge there were political prisoners. They are all criminals, he said, and it was up to the president to decide when prisoners were released - adding that prisoners had already been freed on three recent occasions. The government, he said, was focused on the development of the whole country.
Between 600 and 1,000 journalists, dissidents and monks who led anti-government protests in 2007 are thought to remain behind bars in Burma. In her interview with the BBC, Ms Suu Kyi said all political prisoners must be freed - regardless of whether the government admitted their existence. She said the country had not yet reached the stage where she could say Western investment ought to be encouraged.
There is now a general acceptance that change is under way in Burma, says the BBC's Rachel Harvey in Rangoon, but it is not clear how far or how fast any transition will be.