"The Islamic community of Bosnia takes seriously threats... To (Bosnia's) Muslims and the Grand Mufti Husein Kavazovic," a statement released from his office read.
"We hope that the state's institutions will take up this issue," the statement said.
The appeal was issued after some local media broadcast a video of a Bosnian-speaking man in front of an Islamic State flag threatened to "cut the throat" of Kavazovic, adding that the "mujaheddin are coming to Bosnia."
Bosnia's security minister Dragan Mektic said the authorities were taking the threats "seriously."
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"We are taking and will take additional security measures" to protect Kavazovic, Mektic told reporters.
After the November terror attacks in Paris that left 130 people dead, Kavazovic repeatedly denounced Islamic extremism and radicalisation among Bosnian Muslims, who make up 40 per cent of the Balkan country's 3.8 million people.
Five days after the French attacks two Bosnian soldiers were killed in Sarajevo in a suspected Islamist attack.
Out of some 200 Bosnian citizens who have joined jihadist groups in Syria and Iraq, at least 26 have been killed, but some 50 have returned home, according to authorities.