Unlike earlier operations, the army said the strikes did not target Islamic Jihad, but Hamas, which has de facto control over Gaza and so far has kept out of the violence that erupted this week.
Israel targeted Hamas in strikes on Gaza early Saturday after rockets were fired towards it from the Palestinian enclave, the army said, two days after a fragile ceasefire began.
Hamas, the Islamist movement that has de facto control over the Gaza Strip, has so far kept its distance from the deadly exchanges of fire that erupted this week.
A ceasefire has been in place since Thursday morning following the violent escalation between Israel and Islamic Jihad -- the territory's second most powerful Palestinian militant group.
The Israel Defence Forces (IDF) said it was "currently striking Hamas terror targets" in Gaza, where AFP journalists saw the Israeli strikes and reported retaliation from inside the enclave.
The army said it launched the strikes after "two rockets were fired from the Gaza Strip towards Israeli territory" and were intercepted by air defences.
Palestinian security sources said the Israeli strikes were aimed at two Hamas sites in the north of the territory.
It was the first time Hamas has been targeted since this week's escalation began early Tuesday with Israel's targeted killing of a top Islamic Jihad commander.
That strike triggered almost immediate retaliatory rocket fire from Islamic Jihad at Israel, setting off air-raid sirens and sending Israelis rushing to bomb shelters in the country's southern and central regions.
Israel's military had said around 450 rockets were fired at its territory during the fighting and air defences had intercepted dozens of them.
It then responded with its own airstrikes, saying it had targeted more Islamic Jihad militant sites and rocket- and missile-launching squads.
After two days of violence -- in which 34 Palestinians died but no Israeli fatalities -- a ceasefire was agreed.
But it has so far been precarious, with fire coming from both sides on Friday after the agreement went into effect.
The Gaza Strip is home to two million Palestinians, and Israel and Palestinian militants have fought three wars there since 2008.
Israeli analysts said earlier this week that the focus on Islamic Jihad instead of Hamas was a clear signal that the army sought to avoid a wider conflict in Gaza.
Hamas repeatedly said it would not abandon its ally, but not joining the fight helped it maintain a fragile truce with Israel that has seen tens of millions of dollars in Qatari aid flow into the impoverished Gaza Strip since last year.
On Thursday, Israeli military spokesman Jonathan Conricus told reporters that the army had "wanted to keep Hamas out of the fighting".
"Throughout the operation, we of course between distinguished Hamas and Islamic Jihad. And all of our operations were measured, proportionate and focused only on military assets belonging to Islamic jihad," he said