In a letter to the council president, US ambassador John Bolton accused the government of destroying villages, targeting ethnic minorities and failing to initiate democratic reforms.
He also cited press reports that the authorities in Myanmar - formerly known as Burma - are seeking nuclear power capabilities.
Russia and China blocked the last US attempt to get the Security Council to discuss Myanmar in June - and it was unclear whether they would do so again.
Bolton's letter to Russia's UN ambassador Andrey Denisov, the current council president, was sent two days after the military government extended the house arrest of Suu Kyi, which began in May 2003.
The Nobel Peace Prize winner has spent 10 of the last 16 years in detention.
The military took power in 1988 after violently suppressing mass pro-democracy protests.
It held a general election in 1990, but refused to recognise the results after a landslide victory by Suu Kyi's party.
In Tuesday's letter Bolton said "the United States and other members of the Security Council are concerned about the deteriorating situation in Burma".
China and Russia have blocked
past US moves against Myanmar
Bolton is expected to raise the issue at a Security Council meeting on Wednesday, and the US is hoping for a briefing later this week, a US official said, speaking on condition of anonymity because the letter has not yet been formally discussed.
Procedural rules prohibit the council from taking up issues not on its agenda, allowing nations to block discussions.
Since the last attempt in June, US diplomats have gone to several key capitals to try to convince other governments that the 15-nation council, the most powerful UN decision-making body, should discuss Myanmar.
Close China ties
China has long opposed taking up the Myanmar issue because of its close ties to the country, while Russia is believed to object because of fears that such talks could lead to the discussion of its breakaway Chechnya province.
In the letter, Bolton did not spell out any specific action that Washington is seeking.
He warned, however, that the flow of narcotics from Myanmar is a catalyst in spreading HIV and Aids as well as "potentially destabilising transnational crime".
In addition, Bolton wrote that the military government "has destroyed villages, targeted ethnic minorities, and forced relocations".
He also said its "failure to initiate democratic reforms while repressing political opponents shows the regime's continued intent to maintain power regardless of its citizens' desires".