Asean and the Organisation of Islamic Cooperation (OIC), he said, must not remain silent on the systematic persecution of the Rohingya Muslims.
One online petition calling for such a move has received more than 375,000 signatures as of writing.
That mission was established after an earlier crackdown in Rakhine, in October, also in response to a coordinated attack on security forces by Rohingya militants.
She said, however, that many in Cox's Bazar would say the government's aid so far has been "inadequate". Late a year ago, more than 80,000 Rohingyas had crossed over to Bangladesh to escape an aggressive military offensive in the region after an insurgent attack on border posts.
The foreign secretary also said, "We sent letters not just to global organisations, but to every mission [embassy] as well".
The United Nations yesterday said that almost 164,000 Rohingya have escaped to Bangladesh over the past two weeks in the wake of a massive security sweep and alleged atrocities by security forces and Buddhist mobs against them.
Human rights groups slam Israel for selling weaponry to the Myanmar junta amid intensified violence against Rhingya Muslims, including 100 tanks and light weapons.
Mr Ali said about 10,000 homes had been burned in Rakhine state, a figure that can not be verified as Myanmar has restricted independent access to the state.
Prime Minister Narendra Modi, who concluded his three-day visit to Myanmar on Thursday, expressed solidarity with the government there against the "extremist violence" in the Rakhine state.
But government spokesman Zaw Htay said Myanmar would not negotiate with "terrorists".
Robert Watkins, the United Nations resident coordinator in Bangladesh, said that with the inflow of people showing no signs of abating, "there is now an urgent need for 60,000 new shelters, as well as food, clean water and health services, including specialist mental health services and support for survivors of sexual violence".