An Israeli tank struck two Hamas positions in the Gaza Strip late Sunday after the Israeli army claimed bullets were fired from the Palestinian enclave.
On Sunday night Israel's Iron Dome missile defence system was activated and sirens sounded near the border, but it later turned out these were false alarms.
The army said it was investigating why the systems turned on, but said "unusual machine gunfire towards Israel was identified."
Palestinian security sources said there had been no casualties in the territory of two million that has been under Israeli siege for the past 10 years.
Two observation points belonging to Hamas were struck in the northern part of the enclave, the army said.
It was the second night in a row that Israel had struck the coastal territory.
The strikes came ahead of a planned protest on Friday in which Palestinians have been urged to camp along Gaza's border with Israel.
Last year, a UN report described the power blackouts in Gaza as a humanitarian crisis caused by politics. Some hospitals use generators as back-ups but the system is not infallible.
Hamas's armed wing began a military training operation Sunday which is expected to end Monday morning.
Overnight Saturday, Israel bombed a Hamas position after four Palestinians infiltrated the border and tried to damage equipment.
Israel is wary of Friday's planned protests to mark Land Day, which commemorates the Israeli seizure of thousands of acres of Palestinian lands and the murders of six unarmed Arabs.
The protest is expected to grow from then until around May 14, the date the United States is set to inaugurate its capital in Jerusalem.
President Donald Trump's decision to recognise Jerusalem as Israel's capital and move the embassy there infuriated Palestinians and has been condemned by the UN.