"The ship was monitored and was intercepted in accordance with worldwide law", the military said in a statement, before the vessel, named Freedom for Gaza and carrying 12 people, was taken to the Israeli port of Ashdod.
"The IDF is prepared to target any aggression against Israel and holds Hamas responsible for everything happening in and emanating from the Gaza Strip", the IDF said in a statement.
"The resistance can not allow the occupation to impose a policy of bombing sites and targeting fighters without paying the price", it said in a statement. The video then cuts to separate footage of a shell hitting the post and an explosion.
The men were both claimed as members of the Izz ad-Din al-Qassam Brigades, a violent wing of Hamas.
But Hamas said its fighters were taking part in a live-fire exercise and that Israel would pay for their deaths.
Smoke rises following an Israeli attack on the Gaza Strip as it seen from the Israeli side of the border, May 29, 2018.
Israeli soldiers attacked with force on Monday Palestinian civilians who were protesting Israel's destruction of water holes and pipes that were supplying their villages in the northern Jordan Valley with badly needed water, according to participants in the protest. Violence between the Palestinians and Israel has gained momentum late March, when Gazans started marching towards the fenced border with Israel in a series of protests calling for the right of Palestinian refugees to return to their lands in Israel.