Nearly 100 members of the Salcette Muslim Forum in Margao, located 35 km south of Panaji, took out the march.
The protesters alleged thousands of Rohingya Muslims have been subjected to "torture" and forced to flee their homes in Myanmar's Rakhine state.
They also submitted a memorandum addressed to External Affairs Minister Sushma Swaraj and UN Secretary-General Antonio Guterres.
The memorandum was submitted to South Goa District Collector Anjali Sehrawat.
The forum demanded the UN and Indian government's intervention to stop atrocities against the community.
The outfit said the world body should immediately use its high offices and stop the bloodshed in Myanmar.
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