The clashes broke out when police were trying to evict illegal occupants of a land in Jawahar Bagh by activists, believed to be of Azad Bharat Vidhik Vaicharik Kranti Satyagrahi, on the directions of the Allahabad High Court.
IG (Law and Order) H R Sharma said around 3,000 encroachers pelted stones and later opened fire at the police team as they reached the spot.
In retaliation, the police had to fire after using batons and tear gas at them, he said.
SP (City) Mukul Dwivedi and SHO, Farah police station, Santosh Kumar were killed in firing by the encroachers, Sharma and Mishra told PTI.
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Mishra said at least four dozen people, including, two dozen police personnel, were injured in the skirmishes.
Search operations were on in Jawahar Bagh though activists
of Azad Bharat Vidhik Vaicharik Kranti Satyagrahi were evicted by the joint operation of police, PAC and RAF.
Chief Minister Akhilesh Yadav expressed grief over the incident and announced an ex-gratia of Rs 20 lakh to the family of the deceased policemen.
He also directed that additional police reinforcement be rushed to the area and the guilty be arrested.
Ram Vraksha Yadav, leader of the activists, and the security officer of the group Chandan Gaur managed to flee along with thousands of their supporters, DM Rajesh Kumar said.
The activists used not only hand grenades but also opened fire from automatic weapons after taking position at tree tops, he said.
The area was filled with smoke due to blast of hand grenades and LPG cylinders following which several huts caught fire, the DM said.
Their demands included "cancellation" of election of President and Prime Minister of India, replacement of existing currency with 'Azad Hind Fauj' currency, sale of diesel at the rate of 60 litres for one rupee and petrol at the rate of 40 litres for one rupee.
The high court had, acting on a PIL, recently directed the authorities to vacate the land.