The incident took place in southern Gaza, in the city of Rafah. According to the IDF, no casualties were recorded.
The Palestinian group Hamas denied involvement in the armed incidents.
Prime Minister Benjamin Netanyahu convened consultations with the national security leadership and ordered the army to take"firm measures" against any provocations, but did not threaten to resume war.
The attacks came shortly after Israel announced the identification of the remains of two hostages released by Hamas: Ronen Engel from Kibbutz Nir Oz and Sonthaya Oakkharasri, a worker killed in Kibbutz Be'eri.
The authorities in Jerusalem also announced that the Rafah crossing point on the border with Egypt will remain closed until"further orders", making the return of the bodies of 28 hostages conditional.