Europe's biggest city was under a security lockdown as thousands of police manned barricades and closed streets to stop demonstrations at Taksim, a traditional rallying ground for leftists that saw weeks of unrest in 2013.
Riot police unleashed water cannon and chased protesters down sidestreets in the nearby Besiktas neighbourhood, where they fired off canisters of tear gas, according to a Reuters reporter at the scene.
Several people were detained after demonstrators lobbed stones and bottles at police and set off fireworks.
Citing security concerns, much of Istanbul's public transport had been shut down and police helicopters circled over the city.
Tens of thousands also gathered to march in the capital Ankara, where the mood was more festive.
Critics say President Tayyip Erdogan and the government have become more authoritarian in the buildup to June elections.
Erdogan has previously dismissed protesters as "riff-raff" and terrorists, outraged by the unrest in 2013 that brought unwanted international attention and posed the biggest challenge to his AK Party since it came to power in 2002.
He is aiming for a massive victory for the party in June parliamentary polls, which would allow it to change the constitution and give him broad presidential powers.
The 2013 Taksim protests began as a peaceful demonstration against plans to redevelop Gezi Park, a leafy corner of the square.
After a police crackdown the demonstration spiralled into weeks of nationwide protests against Erdogan's rule.
May 1 is an ancient Northern Hemisphere spring festival and usually a public holiday. In the late 19th Century, May Day was chosen as the date for International Workers' Day. In those countries that celebrate International Workers' Day, the day may also be referred to as "May Day" but it is a different celebration from the traditional May Day.