"We will go to Gaza in late June, after the elections," which are scheduled on June 12, Salih Bilici, spokesman for the Turkish NGO Islamist charity IHH told AFP.
The convoy had initially planned to leave late May to mark the anniversary of the deadly raid against the first flotilla on May 31.
The ferry Mavi Marmara of IHH was the admiral ship of the flotilla when Israeli soldiers attacked in international waters, causing a crisis between Israel and Turkey, and drawing international condemnation.
"We do not want the mission to be jeopardized by possible controversies," of the election process in Turkey, Bilici said.
Turkey's Islamist-rooted Justice and Development Party (AKP) is running for a third term in the elections.
Bilici said participants in the flotilla would leave together but he did not disclose a departure point.
A coordination committee of the international mission dubbed "Freedom Flotilla II", had said last weekend in Athens that the convoy would sail from "a country in Mediterranean."
Bilici said the ferry Mavi Marmara would be in the new convoy too, which will bring together participants from 50 countries in a bid to break Israeli blockade of Hamas-controlled Gaza.
Israel expressed its "concerns" to Turkey about the plans for the new flotilla earlier this week, Israeli officials said.
"We have taken note, we will review", a Turkish diplomat on condition of anonymity said about the meeting between Israel's Ambassador to Ankara Gabby Levy and Turkish officials. Israeli Prime Minister Benjamin Netanyahu also asked the EU to prevent the new fleet.
Relations between Israel and Turkey, once close allies, have sharply deteriorated in recent years amid Turkish Prime Minister Recep Tayyip Erdogan's frequent outbursts against Israeli policies towards the Palestinians.