Thursday’s discovery came the day after three people were killed and dozens more wounded when clashes erupted between Kurdish fighters from the Patriotic Union of Kurdistan (PUK) and Arab and Turkmen demonstrators in Kirkuk.
A Sunni Arab man was killed and two others injured by security forces in the south of the city where armed Arabs and Turkmens were trying to attack Kurdish targets, Yussif's deputy Sirzad Rifaat Qadir said.
Several other people, including a police officer, were also wounded during armed confrontations in the Al-Uruba district of the city, and police have called for reinforcements from the US military that controls Iraq.
"Unknown attackers stabbed two Kurds to death and threw their bodies near a bridge in the centre of the city," Kirkuk police chief Turhan Yussif said, adding that clashes also erupted late on Thursday between police and armed attackers.
Intense gunfire could be heard in the centre of the city, where the streets were deserted and in darkness because of a power cut.
Tensions have been simmering between Kurds, Arabs and Turkmens in this city of almost one million people since the collapse of former Iraqi president Saddam Hussein's regime in April.
Three were killed when a protest
demonstration turned violent
About 2,000 Turkmen and Sunni Arabs staged a protest Wednesday against a push by the city's Kurdish majority to incorporate it into an autonomous Kurdish province but the event soon turned violent.
Three people were killed and 31 injured by shots said to have been fired by PUK gunmen, although the group's Kirkuk chief Jalal Jawhar blamed Saddam loyalists.
The PUK said earlier on Thursday that a gang of about 50 gunmen had tried to attack its offices in Kirkuk, and police said they had arrested four people over the incident.
Last week, thousands of Kurds took to the streets of Kirkuk to lay claim to the city where Saddam's regime settled large numbers of Arabs from the 1970s.
'Connected' academic killed
In the northern city of Mosul, an academic alleged to be affiliated to the deposed Baath government was found dead, a day after he was abducted from his home, according to police.
"Unknown attackers stabbed two Kurds to death and threw their bodies near a bridge in the centre of the city"
Kirkuk police chief
"The body of Dr Abd Allah Jabbar Mustafa, dean of the political science faculty at Mosul University, was found in the Kafaat district" of central Mosul, Haitham Abd Allah, a local police officer, told AFP.
Abd Allah said Mustafa, who was abducted by unknown elements from his home on Wednesday, had not held a senior position in Saddam Hussein's Baath party.
He said police, already investigating a series of similar murders in the city, had launched an inquiry into the latest death.
A lawyer who assisted US forces with legal matters in Mosul was gunned down on 27 December, one day after gunmen shot and killed an influential tribal chief and MP under Saddam's ousted government.
A Turkmen judge was shot dead in the centre of Mosul on 22 December. Two weeks earlier, a judge was killed divided city.