Israeli warplanes hit the Gaza Strip's Islamist rulers Hamas on Saturday after cross-border mortar fire by Palestinian militants, the Israeli army said.

Fighter aircraft hit "Hamas terror targets in the northern Gaza Strip," an army statement said. "Among the targets were weapon storage facilities and an underground infrastructure used by the Hamas terror organisation," the English-language statement said.

There were no reports of casualties. The strikes followed successive rounds of cross-border fire from Gaza on Friday and the launch of balloons fitted with incendiary devices into southern Israel.

Israel retaliated to Friday's first volley with tank fire on what an army statement called a "Hamas military post" in southern Gaza. The latest uptick of violence came after US President Donald Trump enraged Palestinians with a controversial peace plan which would allow Israel to annex swathes of territory in the occupied West Bank.

But it has so far been  on nothing like the scale of flare-ups last year. Israel carried out air strikes on Hamas targets in Gaza early Friday after three rockets were fired the previous evening, causing neither casualties nor damage, the army said.

Hamas and Israel have fought three wars since 2008, but over the past year, the Islamists have gradually shaped an informal truce with Israel, under which the Jewish state has eased its crippling blockade of Gaza in exchange for calm.