Instead, the State Department has called for a de-escalation of tensions between security forces and Rohingya militias, and urged Myanmar's government to expand access to humanitarian aid groups and journalists.
Rohingya Muslims face widespread persecution in Buddhist-majority Burma, where the recent violence has driven hundreds of thousands to seek refuge overseas.
"We request you to take immediate action for cessation of indiscriminate military attack on innocent civilians that is forcing them to leave their home and flee their country to turn into stateless people".
At the upcoming UNGA, Bangladesh has a chance to show the worldwide community what is really at stake, and make the case that it is time to put some serious pressure on Myanmar - the kind that Yangon can not ignore.
"We want peace and a friendly relation with neighbouring countries...(but) we can not allow and accept any kind of unjust and our protest will continue to this end", Hasina said after visiting a Rohingya refugee camp near the border town of Ukhiya in Cox's Bazar district.
Before the current crisis erupted, between 300,000 and 500,000 Rohingyas were living in Bangladesh, out of whom only 32,000 enjoy refugee status and live concentrated in refugee camps in Cox's Bazar district in southeastern Bangladesh.
She further said that Myanmar must take back its citizens now sheltered in Bangladesh, The Daily Star reported.
Attacks by a Rohingya insurgent group on police posts and an army base in the north of Rakhine on August 25 provoked a military counter-offensive that refugees say is aimed at pushing Rohingya out of the country.
Observers say the violence is being carried out by the Myanmar military.
On Monday, UN High Commissioner for Human Rights Zeid Ra'ad al-Hussein described the military crackdown on Rohingya as a "textbook example of ethnic cleansing". But Myanmar authorities deny that their forces have been setting the fires.
At least 370,000 Rohingya Muslims in Myanmar fled to Bangladesh from facing violence and human rights violations as pressure against the government mounts this week.
But a spokesperson for the NLD said she was not aware of the reason for the Aung San Suu Kyi's withdrawal from this year's General Assembly.
Turkey has been at the forefront of providing aid to Rohingya refugees and President Recep Tayyip Erdogan has said he will raise the issue at the UN.
According to her spokesman, State Counselor Aung San Suu Kyi will focus attention on the "Rakhine terrorist attacks", and will not attend the United Nations session.
In recent days Suu Kyi has faced calls to revoke her 1991 Nobel Peace Prize over her government's violent crackdown on the Rohingya, which the United Nations human rights chief called "a textbook example of ethnic cleansing".