"The IDF is prepared for a variety of scenarios and is determined to act against the terrorist operatives and will continue to carry out its mission to protect the citizens of Israel", the statement said.
The Gaza Strip has been under Israeli blockade for over a decade, which Israel says is necessary to prevent Hamas from obtaining means to attack.
The Israel-Gaza border fell quiet on Wednesday under a de facto ceasefire after the most intense flare-up of hostilities between Palestinian militants and Israel since a 2014 war.
Al Hayya said in a statement early Wednesday that there had been considerable mediation efforts - an apparent reference to Egyptian-led talks - resulting in "a consensus to return to the ceasefire understandings of the Gaza Strip".
Al-Haya said militant groups in Gaza will commit to the ceasefire as long as Israel does.
Armed Palestinian groups are taking responsibility for the barrage of launches, which left three Israeli soldiers injured on Tuesday. Some were shot down by Israel's Iron Dome rocket interceptor system and others landed in empty lots and farmland. One exploded in a kindergarten yard, damaging walls and scattering debris and shrapnel around the playground, about an hour before it was scheduled to open for the day.
But he said "the risky escalation" can't be divorced from two months of protests at the Gaza fence in which some 110 Palestinians were killed and large numbers injured by Israeli fire.
Tuesday's incidents followed weeks of deadly demonstrations and clashes along the Gaza-Israel border, beginning on March 30. The BBC report of the same events notes right away in the sixth paragraph that "UN and human rights officials have accused Israel of using disproportionate force" - the Times cites no human rights organizations.
On Sunday, an Israeli tank fired on a Islamic Jihad observation post and killed three people, according to Al Jazeera.
The United States has called for an emergency meeting of the UN Security Council to discuss the latest attacks on Israel from the Gaza Strip, the USA mission to the United Nations said Tuesday.
Hamas had largely abided by an Egyptian-brokered truce that ended the seven-week Gaza war four years ago.