The two sides have been engaged in sporadic fighting since Saturday around the city, home town of slain longtime dictator Moamer Kadhafi, whose regime was toppled in a 2011 NATO-backed revolt.
"Twelve heroes of the Libyan army have been killed treacherously at Noufliyeh", a stronghold of the jihadists, who have controlled large areas around Sirte since February, said authorities in Tripoli.
That was a reference to the Fajr Libya alliance, which includes Islamists and which has installed a government in Tripoli opposed to the internationally recognised legislature and cabinet based in the eastern city of Tobruk.
There were no immediate details on possible IS casualties.
The Tripoli-based defence ministry said the clashes erupted at Sirte on Saturday after IS closed off the coastal road there to protest the arrest of jihadist leaders.
Libya has been plagued by chaos since the end of the 2011 revolt that toppled Kadhafi, with heavily armed militias battling for control of its cities and oil wealth and the rival governments and parliaments vying for power.
Sirte, 450 kilometres (280 miles) east of Tripoli, has been a bastion of Islamist extremism, with rival groups positioned in the Mediterranean city.
A parliamentary source in Tobruk told AFP a delegation from there "will participate in tomorrow's dialogue session, although we don't have a clear vision about what may come out of these discussions".
The UN mission in Libya, meanwhile, urged "all the different sides to the conflict in Libya... To refrain from further military escalation and focus their efforts instead on combating this common enemy", referring to IS.
Feeding on the lawlessness that has gripped Libya, IS has extended its influence there from Syria and Iraq where it holds territory on which it has installed a "caliphate".
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