Police tried to stop around 200 protesters in the Gayrettepe district on the European side of Istanbul who wanted to walk to the famous square in spite of the ban by city authorities, an AFP journalist reported.
The protesters - made up of left-wing groups - unfurled anti-government banners against the result of the April 16 referendum, which handed President Recep Tayyip Erdogan expanded powers.
"Long Live May Day, No to dictator!" the banners read. At least one protester was detained, according to the AFP journalist.
Police detained two women who attempted to unfurl banners at the square, the private Dogan news agency reported.
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At least 13 people who attempted to defy the ban on Taksim were detained, the state-run Anadolu news agency reported.
Members of the group were wearing May Day T-shirts and chanting slogans: "No to Taksim ban."
In the secular Istanbul district of Besiktas, at least 60 protesters were detained, an AFP photographer reported.
Some 30,000 police were on duty in Istanbul alone, with the governor's office urging citizens not to heed calls for protests in non-official areas.
Metro lines did not stop at Taksim square, which was a rallying ground for May Day celebrations until 1977, when at least 34 people were killed during demonstrations.
Authorities later opened up the square for celebrations but it was shut down again after it played host to anti- government protests in 2013 targeting Erdogan, then prime minister.
"Our people were massacred on May Day in 1977, workers were massacred," a women protester who gave her name as Sevim told AFP.
This year's May Day celebrations also come after the 'Yes' camp won last month's referendum with 51.41 per cent of the vote against 48.59 per cent for the 'No' camp.
The opposition have alleged major irregularities but its complaints were thrown out by the election commission and a top court.
Yunus Ozgur, another demonstrator, said he wanted to march to Taksim square to protest "irregularities" during the referendum.
"We are frustrated," he said. "Taksim has a political meaning. They (authorities) are scared of this. Taksim is ours.
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