A decision on exactly when a departure might take place was to be taken later on Saturday, Audrey Bomse of the Free Gaza Movement (FGM) told the AFP news agency.
"A final decision is expected to be made about the flotilla's departure as some people are still trying to negotiate their way on the Turkish ship" in the flotilla, Bomse said.
It was expected that the flotilla would set sail on Saturday but only attempt to land in Gaza on Sunday.
The flotilla "will not approach Gaza until tomorrow [Sunday] because we don't want to enter during the dark. These problems won't stop us," Bomse said.
Thomas Sommer-Houdeville, a French activist on board one of the boats, said: "We are currently sailing to the limits of Cypriot waters to try and negotiate with authorities."
Sommer-Houdeville said that the Cyprus authorities had briefly detained the captians of the boats that were aiming to take the politicians on board on Friday night.
He said that the captains were later released.
The flotilla organisers have said that Cypriot officials have not fulfilled a pledge to let the boats sail from its waters. The activists have alleged that Israeli pressure has swayed the authorities.
Hamas, the de facto rulers of the Gaza Strip, have said that the flotilla was about to make history, sending "a strong message that the blockade imposed on the Gaza Strip ... will be broken."
Israel said the boats were embarking on "an act of provocation" with the Israeli military rather than providing aid, and that it had issued warrants to prohibit their entrance to Gaza.
It asserted that the flotilla would be breaking international law by landing in Gaza, a claim the organisers angrily denied.
Israel has said that it will intercept the boats and detain those on board in the port of Ashdod.