The Swedish-flagged ship Juliano left Greece Wednesday on its way to the Gaza Strip a day after it was turned back by the Greek coast guard.
Some 20 activists are on board the vessel, which was damaged last week while sitting in a Greek port. Organizers blamed Israel for the problems.
The Juliano will rendezvous with Dignite al Karama, a small French boat with eight activists aboard that left Greek waters Tuesday as the first vessel of the Gaza-bound flotilla attempting to break the Israeli naval blockade of the coastal strip.
The ships are marking the May 31, 2010 raid of a similar flotilla by Israeli commandos. Nine Turkish activists were killed in the subsequent melee, including a Turkish-American dual citizen.
Israel says the flotilla is illegal and military action to keep it from arriving in Gaza is legitimate. Israel maintains the blockade to keep weapons from flowing into Gaza, which is controlled by Hamas, and also as leverage to secure the freedom of Gilad Shalit, a kidnapped soldier held by Hamas since 2006.
Human rights groups say the blockade keeps out basic foods and medicines, although the Obama administration says its conditions have eased considerably in the last year.