Jihadist websites also posted pictures showing armed men sitting in front of microphones in a broadcasting studio and brandishing Kalashnikov assault rifles.
"They took Radio Sirte yesterday (Thursday). Since then they have been broadcasting (verses from) the Koran and speeches by (IS chief Abu Bakr) al-Baghdadi," a resident of the central city told AFP by telephone.
The resident said speeches of IS spokesman Abu Mohammed al-Adnani were also being played on the air.
A former local administration official said the gunmen have set up a headquarters in the centre of the city, and voiced concern that they could declare an Islamic emirate in Sirte.
"They could take advantage of the absence of any central government authority to transform the city into an Islamic emirate as they did in Derna," an eastern city held by jihadist groups including IS.
The man, who declined to be named, said the gunmen apparently seized the radio "as a first step to communicate with the population".
"The situation in Sirte is very complex," he said, because many radical groups have a foothold there.
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Since the 2011 uprising that toppled and killed dictator Moamer Kadhafi, Sirte, the former strongman's hometown has become a stronghold of extremist groups.
Sirte is a bastion of Ansar al-Sharia, an Islamist blacklisted by the United Nations and the United States.
And militias of the Islamist-backed Fajr Libya (Libya Dawn) coalition control some parts of Sirte, and launched attacks against key oil installations nearby in December.
On Friday, gunmen raided the Al-Bahi oil installation south of Sirte, causing heavy damage but no casualties before being repelled, guards at the privately run site said.
The security spokesman for Libya's oil facilities, Ali al-Hassi, pointed a finger of blame at IS, whose militants attacked the nearby Al-Mabrouk field on February 3.
Powerful militias, backing rival governments and parliaments, have been battling for control of key cities and the country's oil riches since the uprising four years ago.
Taking advantage of the chaos, IS has claimed a string of deadly attacks. The latest targeted a luxury hotel in Tripoli on January 27, when nine people were killed, five of them foreigners.