"The whole world is now watching Burma," the prime minister told reporters at the Labour party's annual conference in Bournemouth. "I hope the security council will meet immediately, meet today and discuss this issue and look at what can be done."
The foreign secretary, David Miliband, urged the Burmese authorities to show "restraint", adding that it was important "we continue to be a strong voice".
The EU has warned Burma's military junta that it faces tougher EU sanctions if it uses force to crush growing anti-government protests.
In a statement issued by its Portuguese presidency, the 27-member EU said: "The EU further underlines to the authorities ... that it will reinforce and strengthen the existing sanctions regime, should they resort to using violence against the unarmed and peaceful demonstrators."
Existing EU sanctions include a travel ban on Burma's leaders, an arms embargo and a ban on military cooperation.
Foreign governments and religious leaders have urged the Burmese junta to deal peacefully with the situation.
They have included the Dalai Lama and Archbishop Desmond Tutu, both of whom, like the detained opposition leader Aung San Suu Kyi, are Nobel peace prize laureates.
The US president, George Bush, yesterday announced new sanctions against Burma, including visa restrictions against members of the government.
In a speech to the UN, Mr Bush accused the regime of imposing "a 19-year reign of fear" and added: "Americans are outraged by the situation in Burma."
Mr Brown, who described Ms Suu Kyi as a true hero in his recent book, called on the security council to discuss Burma in early September.
His renewed request places Burma's ally China in a difficult position. Beijing traditionally dislikes anything that smacks of interference in a county's domestic affairs.
Before the recent protests, China, Russia and South Africa indicated that the UN's human rights council was the appropriate place for addressing the situation in Burma when, in January, they voted against a security council resolution condemning Burma.
Human rights groups are calling on the UN to take up the issue of Burma again.
"Those who blocked action at the security council said that the situation in Burma was the responsibility of the human rights council," Human Rights Watch, based in New York, said.
"Now it is time for them to show that they meant what they said. The council cannot simply sit back and watch as the situation in Burma deteriorates."
