Around 500 people took part in the rally on Saturday evening, police said early Sunday.
Protesters in the city's Connewitz district threw stones and fireworks, they said, with two officers suffering injuries.
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The rally was broken up after less than an hour but spontaneous demonstrations followed during the night, with protesters setting fire to bins and a police car.
Police are investigating 15 suspects for breach of the peace, damage to property and resistance to law enforcement officers.
The protests began Wednesday.
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The rallies aim to denounce what the far-left in particular perceives as the “gentrification” of Leipzig, with the purchase of many apartment buildings by groups of financial investors.
Demonstrations on Friday evening also turned violent, with protesters throwing bottles, fireworks and stones. Eight police officers were slightly injured, six police vehicles damaged and a police station pelted with paint bags and stones.
Leipzig mayor Burkhard Jung described the riots Saturday as a “serious setback” for the debate around affordable housing.
“You don't create living space by attacking police officers and setting fire to barricades,” he said. “This violence must be condemned in the strongest possible terms.”