The High Electoral Board announced in a written statement its decision by a 10-1 vote to reject three requests by the opposition.
Thousands have protested in Istanbul and Ankara since Sunday's referendum, which has set into motion the transformation of Turkey's system of government from a parliamentary to a presidential one.
Electoral board head Sadi Guven said the objections would be evaluated later on Wednesday.
He said the electoral board's last-minute decision to allow unstamped ballots had prevented proper record-keeping, meaning that it was now impossible to determine how many invalid or fake votes may have been counted.
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The petitions had been filed by the main opposition Republican People's Party (CHP), the Peoples' Democratic Party (HDP) and the Patriotic Party.
Turkey's top election authority on Tuesday rejected an opposition bid to annul the referendum on expanding President Recep Tayyip Erdogan's powers after complaints of vote-rigging, state media reported.
"The main opposition party not recognizing the results is not an acceptable thing", Yildirim said.
Before the announcement, Prime Minister Binali Yildrim said the opposition had the right to file objections but said that calling for street protests was unacceptable. He added that "we expect the main opposition party's leader to act more responsibly".
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The protesters on Wednesday evening chanted "Thief, Murderer, Erdogan" and "Don't be silent, shout out, "no" to the presidency". Unofficial results, which the opposition said it would challenge, showed a narrow victory for him with 51.4 percent of votes cast in favour.
The official results are due to be released at the beginning of May.
Observers from the Organisation for Security and Cooperation in Europe (OSCE) and the Council of Europe said Sunday's referendum had been an uneven contest.
On Monday, the White House said in a statement that Trump called Erdogan to congratulate him on his referendum victory and to thank him for supporting a USA missile attack on Syria in response to a chemical attack by Syrian government forces on April 4. "From the German government's point of view, Turkey must ... clear up the questions that have been raised".
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Foreign Minister Mevlut Cavusoglu said on Wednesday a critical report by European observers on the referendum contained several mistakes which he believed were deliberate.