Two Palestinians were killed on Tuesday in an Israeli airstrike targeting a group of citizens in Beit Lahia town in northern the Gaza Strip.
The group called to immediately release the captains who were arrested by the Israeli naval forces in global waters as they tried to break the blockade imposed on Gaza.
Hamas said in response that "Israel is responsible for this entire escalation", and warned that "the resistance will not accept the [Israeli] policy of attacking its positions and fighters without Israel paying a price".
The army issued orders to Israelis living on the Gaza periphery to be ready to enter the shelters in case rockets start falling from Gaza.
There have been reports about talks between Palestinian factions, Egypt, the United Nations and Israel to reach a long-term truce in the besieged enclave. It then cuts to footage of a shell hitting the post and an explosion.
Hamas' military wing, the Ezzedine al-Qassam Brigades, confirmed in a statement that the dead men were its fighters and named them as Ahmad Murjan and Abdel-Hafez al-Silawi.
"The resistance can not allow the occupation to impose a policy of bombing sites and targeting fighters without paying the price", a Hamas statement said.
Israel's security cabinet discussed the proposal on Sunday, but afterwards ministers said only that the Israeli military was "prepared for any scenario".
The ongoing popular demonstrations have been violently suppressed by Israeli forces, who have killed 160 Palestinians and injured over 17,000 more, according to numbers from the Gaza Ministry of Health.
Two ships which had sailed from Europe to break the illegal siege on Gaza were captured by Israel last week.
"This is a very serious episode", the Hamas statement said, adding that it holds Israel responsible.
Israeli forces stop and search a Palestinian boy at the entrance of Damascus Gate, outside Jerusalem's Old City.