Hamas militants fired a dozen projectiles at Israel overnight, the Israeli army said on Wednesday, in what the territory's rulers said was their response to Israeli targeting of Palestinian civilians.
The projectiles, which Israeli media said included rockets, caused no casualties or damage.
Three of them were destroyed in flight by Israel's Iron Dome air defence system, an army spokesman said.
Hamas said its military wing was retaliating against Israeli fire against Palestinian civilians, which has seen at least 134 Gazans killed since protests along the border began on March 30. There have been no Israeli deaths.
"The occupation's escalation and its targeting of the peaceful Palestinian protesters as well as the Palestinian fighters prompted [an] immediate response," Hamas spokesman Fawzi Barhoum said.
"Every silly measure taken by the Israeli occupation against the Palestinians proves the failure of the Israeli policies and miscalculation of the Israeli plans," Mr Barhoum added.
Late on Tuesday, an Israeli air strike and tank fire targeted a vehicle belonging to a Hamas official "heavily involved" in launching kites and balloons fitted with incendiaries over the border, the army said.
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Two Hamas observation posts in northern Gaza were also hit, the army said. There were no reports of casualties on the Palestinian side.
The fire kites and balloons have caused huge crop losses on Israeli farms near the border, prompting Israeli threats to demand compensation from the West Bank-based Palestinian Authority.
Since March 30, Gazans have been demonstrating along the heavily guarded border in protest at Israel's decade-long blockade of the territory and in support of the Palestinians' right to return to lands they fled or were driven from during the war surrounding the creation of Israel in 1948.
The demonstrations peaked when at least 62 Palestinians were killed as thousands approached the border fence in protest at Washington's moving of its embassy to Israel from Tel Aviv to the disputed city of Jerusalem on May 14.
Israel insists the whole of Jerusalem is its "eternal indivisible capital", but the Palestinians claim the eastern sector, which Israel occupied in the Six-Day War of 1967 and later annexed, as the capital of their future state.