The Sammilito Islami Dal, an alliance of Islamist parties, has demanded sending back the French ambassador to Dhaka in protest against comments made by Emmanuel Macron on Islam.
Leaders of the Islamist alliance warned of 'tougher movement' if their demand is not fulfilled immediately.
Supporters of Sammilito Islami Dal demonstrated after offering Jum'a prayer at Baitul Mukarram national mosque.
Vice-President of the alliance Abu Taher Jihadi Al Kashemi said that no one can stay in this country after defaming Prophet Muhammad (PBUH).
Jafarullah Khan, Secretary-General of the Alliance, said France will be severed into several parts just like the Soviet Union.
"They (France) have slammed Prophet Muhammad, we're requesting all to boycott their products," Khan said.
Protesters also urged the government to summon Ambassador Jean-Marin SCHUH and ask him to apologise in public.
Earlier this month, French President Macron pledged to fight "Islamist separatism", which he said was threatening to take control in some Muslim communities around France.
His comments, in addition to his backing of satirical outlets publishing caricatures of the Prophet Muhammad, has led to a social media campaign calling for the boycott of French products from supermarkets in Muslim countries.
Hashtags such as the #BoycottFrenchProducts in English and the Arabic #ExceptGodsMessenger trended across countries including Kuwait, Qatar, Palestine, Egypt, Algeria, Jordan, Saudi Arabia and Turkey.