The Supreme Electoral Board unanimously rejected the request from the Republican People's Party (CHP), which alleged the incumbent Justice and Development Party (AKP) had won by rigging votes.
The decision is the latest blow to the CHP, which lost a bid for a vote recount of the March 30 poll last week.
The CHP's mayoral candidate Mansur Yavas said the party would take "every legal step at its disposal" to challenge the decision, including taking the issue to the Constitutional Court.
The Islamic-rooted AKP scored significant victories across Turkey in last month's local polls, winning the key prizes of Ankara and Istanbul in votes seen as a referendum on the 11-year-rule of Prime Minister Recep Tayyip Erdogan.
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His government has been rocked by a spate of wiretaps and social media leaks implicating Erdogan in graft and exposing high-level security talks weighing military action in Syria.
But opposition parties claim the polls were marred by irregularities including ineligible votes, widespread power blackouts during vote counting and misreporting of results.
The mayor has rejected claims of any irregularities.