In a separate incident, a man was killed when he was run over by a police water cannon vehicle.
The authorities prevented all public access to Taksim Square in the centre of the city -- the traditional focus for protests -- and the usually bustling area was deserted save for police.
Hundreds of labour and union activists, brandishing slogans promoting workers' solidarity, took part in an officially-sanctioned action at a vast market ground in the outlying district of Bakirkoy close to the international airport.
Police also used water cannon and tear gas on protesters in the district of Sisli who were trying to march on Taksim, another AFP photographer said.
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The state-run Anatolia news agency said 36 people were detained in Sisli and the neighbouring district of Besiktas as they tried to march on Taksim, reports said.
The man who was killed was run over by a police water cannon vehicle, known by its Turkish acronym TOMA and which have become ubiquitous in recent years as the police crack down on protests.
Access to Taksim, the main hub in the European side of the city, was cut off by an interlocking network of police barriers. The square, usually filled with hundreds of people, was completely empty save for a few police.
The Istanbul governor's office had said 24,500 members of the Turkish security forces would be on duty in the city on Sunday "to provide for the security of citizens".
May Day comes at a time of particular tension in Turkey after a succession of deadly attacks this year blamed on jihadists and Kurdish militants.
Meanwhile, Turkish police detained four suspected Islamic State jihadists who were allegedly planning an attack on May Day celebrations in the capital Ankara, the state-run Anatolia news agency said.