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At least 1,000 protesters thronged Besiktas on the European side of the city while on the Asian side around 2,000 demonstrators marched through Kadikoy, another staunchly secular and anti-Erdogan neighbourhood, AFP correspondents said.
The main opposition Republican People's Party (CHP) and the pro-Kurdish Peoples' Democratic Party (HDP) said they would challenge the results from most ballot boxes due to alleged violations.
There has been anger among 'No' supporters over last minute changes to the voting procedures but the authorities insist the referendum was conducted cleanly.
"We will not make you president" and "We are shoulder to shoulder against fascism," the protesters in Kadikoy chanted, as they marched towards the offices of the Supreme Election Board.
Others brandished viral hashtag slogans from the referendum night like "The 'No' is not finished" and "'No' has won".
In Besiktas, protesters held pamphlets with the words "We are right, we will win".
In homes lining the route of the protest, people bashed pots and pans with kitchen utensils from the windows of their apartments to show solidarity.
Police generally kept a low profile on the sidelines of the protest but warned against using offensive slogans.
Smaller protests were also held in other Turkish cities and Turkish media reports said that 13 people were detained in a protest in the southern Mediterranean city of Antalya.
The 'Yes' camp won 51.41 percent in Sunday's referendum, in a narrower than expected victory, according to complete results released by election authorities.