Moves to board the ship came three hours after the navy had first made radio contact with the two vessels, warning them not to continue into naval territory which was under "a maritime security blockade in accordance with international law."
Organisers says the Irish Saoirse and the Canadian Tahrir were in the final stage of their voyage to Gaza, when they were contacted by the navy just before 1100 GMT at some 50 nautical miles from the shore.
The last time a boat tried to reach Gaza was in July when a French-flagged yacht, the last remaining boat of an earlier flotilla, was intercepted by the Israeli navy some 40 nautical miles off the coast.
Activists organised a major attempt to break the Israeli blockade in May 2010, when six ships led by the Turkish Mavi Marmara tried to reach Gaza.
Israeli commandos stormed the flotilla some 80 nautical miles off Gaza. The botched raid left nine Turkish activists dead and sparked a diplomatic crisis with Ankara, which expelled the Israeli ambassador and has cut military ties with the Jewish state.
Organisers of the current flotilla, dubbed Freedom Waves to Gaza, said they had made their plans in secret, in a bid to prevent Israeli interference.
Israel has vigorously defended its right to maintain a blockade on Gaza, saying it is necessary to prevent weapons from entering the coastal territory, which is run by the Islamist Hamas movement.