Ferries were cancelled and metro stations closed to cope with two crowds on either side of the Bosphorus.
Muammer Guler, Istanbul's governor, put the number of arrests at "more than 100" as participants in one of the rallies, organised by Disk and several other unions, tried to march on the square in defiance of a ban.
Union leaders later managed to strike a deal with police, allowing a limited group of demonstrators access to the square.
Suleyman Celebi, Disk's president, said: "We will only be a few thousand marching up to Taksim Square, but we are millions in our hearts."
The organisation said in a statement that six union leaders, including Musa Cam, its secretary-general, were among scores arrested earlier near the Inonu Stadium, just down the hill from Taksim Square.
The arrests came against a backdrop of tensions between the army and government over the country's disputed presidential election, on which Turkey's highest court was expected to deliver a ruling later on Tuesday.
The late 1970s were a time of rising tensions between Turkey's rightwing government and its leftwing unions.
- On May 1, 1977, 500,000 members of the country's trade unions rallied in Taksim Square in central Istanbul.
- Soon after the peaceful demonstration began, members of the police and army were seen firing into the crowd.
- Thirty-six people were killed, hundreds were injured in the violence; many were crushed in the stampede to avoid the shooting.
- Turkish police charged 98 people over the incident. All were acquitted.
Several hundred people gathered chanting "Long Live May Day," "We will not bow to pressure," and "Shoulder to shoulder against fascism" before being dispersed by police, who moved in on any group attempting to march to the square.
Dogan Halis, a health workers' union leader, said in a brief speech that ended when officers bundled him into a police vehicle: "We do not deserve this, Turkey does not deserve this. You are giving a shameful image of Turkey, that of the military coups of 1971 and 1980."
Guler had rejected several earlier Disk demands to officially hold their rally on Taksim Square, citing "intelligence that many illegal organisations are planning to go there... [to] take on the police".
In another area near the square, the Okmeydani district, about 1,000 demonstrators armed with sticks and stones faced off against a police barricade.
"We have seen this theatre many times... [there is] no way other than democracy"
Srimedya, Bursa, Turkey
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Buses full of of demonstrators coming from Ankara who were prevented from crossing the Bosphorus bridge to join the rally on the European side, gathered in an area know as the Mustafa Kemal neighbourhood in Umraniye.
Other buses were stopped at toll booths at the Istanbul end of the motorway from Ankara, and Disk said police were forcing many of them back to the capital.
Disk accused police of throwing tear gas canisters inside some of the buses and said one woman was hospitalised with a broken arm and cranial trauma.
Another May Day rally in Istanbul, held in Kadikoy Square on the Asian side of the city and organised by the Turk-Is labour confederation, was said to have gone ahead without incident.
Officials said about 17,000 police have been deployed in Istanbul for the demonstrations.
Two days ago, in protests linked to the disputed presidential election, more than one million people demonstrated in Istanbul against the government and in favour of secularism and democracy.