Bangladesh as the major recipient of Rohingya refugees, wanted to have in-depth discussion with Indonesia regarding the problem, Marty said.
Hundreds of thousands of Rohingya Muslim refugees have migrated to Bangladesh.
"The point is how we could prevent the problem from becoming more complicated," he added.
In the meeting, the two foreign ministers also discussed the bilateral relations between Bangladesh and Indonesia.
Minister Marty Natalegawa also held a bilateral meeting with Erika Feller, the Assistant High Commissioner of the United Nations Refugee Agency (UNHCR) on the sidelines of the Bali Process on People Smuggling, Trafficking in Persons and Related Transnational Crime.
The UN agency expressed appreciation to Indonesia for the country`s contribution to the implementation of the Bali Process and to helping find solution to the Rohingya issue in Myanmar.
"They appreciate what we have contributed in the Bali Process and our contribution to finding solution to the Myanmar problem," the minister said.
Marty Natalegawa and his Australian counterpart are co-chairs of the Fifth Bali Process meeting.