Speaking as EU foreign ministers met to discuss proposals for more sanctions against Burma, Mr Brown said the UK would be pressing for "tough" measures.
But he revealed that he had written to world leaders proposing an economic recovery package for Burma if democracy was introduced to the country.
In a statement, he said: "I want to be clear, if this process of change begins we stand ready, as the international community, to support the recovery of Burma with aid and other support."
In the meantime Mr Brown is pushing for an EU ban on future investment in Burma and sanctions against goods such as timber, gems and metals.
He said: "I believe the gaze of the whole world will remain on the Burmese regime as long as people know about the violence being practised against Burmese citizens, the repression against religious leaders and the loss of civil liberties suffered by Aung San Suu Kyi and so many people.
"That is why today we will be pressing at the EU for sanctions against the Burmese regime."
He was speaking after receiving human rights campaigners and Buddhist monks who delivered an international petition with more than three-quarters of a million signatures calling on the UN security council to oppose the violent crackdown on demonstrators in Burma.
The prime minister welcomed the petition. He said it "sends a strong message that people all over the word will stand with the people of Burma".
He added that human rights abuses were still taking place in Burma following the bloody crackdown against last month's protests. Last week it emerged that an active member of Ms Suu Kyi's party had died under interrogation, and more pro-democracy leaders were arrested over the weekend.
Earlier today the UN envoy Ibrahim Gambari said that recent reports of arrests in Burma were "extremely disturbing".
Speaking in Thailand at the start of a tour of Asian countries to resolve the crisis in Burma, Mr Gambari called on the junta to halt its crackdown immediately.
Ahead of Mr Gambari's arrival in Bangkok, Burma's military rulers eased more restrictions imposed after the protests last month. Weekend internet access was restored but a block on foreign news sites remained in place.
Mr Gambari travels next to Malaysia, Indonesia, Japan, India and China before returning to Burma.
He called for the release of all political detainees, including those who were arrested during the recent protests, and asked for access by the International Red Cross to people in detention.
Earlier this month Mr Gambari met Burma's reclusive leader, General Than Shwe, during a four-day visit in which he also met Ms Suu Kyi twice. Gen Shwe has since agreed to meet Ms Suu Kyi but only if she rejects calls for sanctions and drops her confrontational stance against the regime. Ms Suu Kyi, who remains under house arrest, has rejected the offer.
