The US has presented a draft resolution to the UN Security Council, calling on Burma to ease repression and free opposition leader Aung San Suu Kyi.
UN envoy Ibrahim Gambari recently met Aung San Suu Kyi
Washington says the situation in Burma constitutes a threat to international peace and security.
Burma has been under the control of a military government for 40 years.
Elections in 1990, which produced a landslide victory for Ms Suu Kyi's National League for Democracy Party, were ignored by the ruling generals.
Ms Suu Kyi has spent most of the past 17 years under house arrest.
The US has successfully lobbied to get Burma considered by the Security Council, according to the BBC's UN correspondent Laura Trevelyan.
It has now circulated a draft resolution noting the council's "grave concern that the overall situation in Myanmar [Burma] has deteriorated and poses serious risks to peace and security in the region."
The resolution urges the Burmese government to release all political prisoners, including Nobel Peace Prize winner Aung San Suu Kyi, as well as lifting constraints on political leaders and allowing parties to open offices.
Aung San Suu Kyi is still under house arrest
It also calls for an end to arbitrary executions and the rape of women and girls, and condemns attacks by the Burmese military on the Karen people.
"The people of Burma have been suffering for decades. The efforts that others have undertaken, including neighbours in the regions, have really not come to any success," said acting US ambassador Alejandro Wolff.
"The time has come for the Security Council to support the efforts of the special envoy, Under Secretary-General Gambari, who believes this sort of act will help him."
Mr Gambari last visited Burma in November, for a four-day visit in which he met Ms Suu Kyi and urged the country's military government to take steps towards democratic reforms.
It remains to be seen how this draft resolution will fare, our correspondent says. American diplomats hope there will be a vote this week, but they face stiff opposition.
"We think that it's not a proper issue to discuss in the Security Council," said Russia's ambassador to the UN, Vitali Churkin. "That's why we voted against putting it on the agenda of the Security Council."
"We don't think that any action taken by this council will be conducive to promote any solution of the Myanmar issue," added China's deputy UN ambassador Liu Zhenmin.
Russia and China, both permanent members of the council, with the power to veto decisions, have long argued that the situation in Burma does not constitute a threat to international peace and security.