The demonstrations began in smaller numbers after Sunday's vote with clattering pots and pans, but have since drawn thousands of participants expressing outrage at alleged voting irregularities.
In a direct response to the board's decision, the CHP said on Wednesday the party would employ all means to appeal the results of the referendum.
"Calling people to the streets by using various communication channels and refusing to recognize the results is never acceptable", Yildirim said.
Those protests were sparked by plans to uproot trees in Istanbul's Gezi Park to build a shopping mall.
Turkey's Supreme Election Board rejected on Wednesday all opposition objections to the results of last Sunday's constitutional referendum, which was passed by 51.4 percent of Turkish voters to officially transfer the country into a presidential regime.
Deputy chairman Bulent Tezcan said Friday that his Republican People's Party, or CHP, would seek a cancellation of the electoral board's controversial decision at the Council of State.
He says the party's next stop is Turkey's constitutional court and, if it is unsuccessful there, then the European Court of Human Rights.
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Turkey's bar association said this week that the last-minute decision by the YSK electoral board to allow the unstamped ballots was clearly against the law, prevented proper records being kept, and may have impacted the results.
Prime Minister Binali Yildirim, whose post will cease to exist once Erdogan's all-powerful presidency proposed under the referendum comes into effect, said everyone had a right to complain - but it would not change the outcome.
The CHP and the pro-Kurdish HDP party, which says millions of unstamped ballots were accepted, have said they could also appeal the referendum result at the European Court of Human Rights if their legal challenges fail in Turkish courts.