The Israeli military says its aircraft have targeted Palestinian militant sites in the Gaza Strip in response to continued rocket fire on southern Israel.
The two sides agreed a ceasefire that came into force early on Tuesday morning local time.
However as with previous deals it has not proved complete.
Rocket fire has continued sporadically with retaliatory air strikes but there are no reports of casualties.
Local sources in Gaza say that farmland was hit by overnight Israeli strikes in Gaza City and Khan Younis in the south. They added that Hamas, which governs Gaza, was trying to convince small militant groups to keep to the truce.
The Israeli army says that one rocket landed near Netivot and another was intercepted by its Iron Dome Missile Defence System, near Beersheva.
It says that since the truce came into effect a total of nine rockets and mortars have hit and two have been intercepted.
Schools in southern Israel have again closed as a safety precaution after opening on Wednesday.
At least 25 Palestinians were killed in four days of Israeli air strikes which began on Friday. Israel says 35 people were injured in Palestinian rocket attacks.
Israeli Prime Minister Benjamin Netanyahu has blamed Iran for the latest violence.
Speaking to the Israeli parliament on Wednesday night he accused Tehran of arming and financing militants in Gaza and again warned of the dangers of Iran's nuclear programme.
The latest cross-border violence was triggered by an Israeli air strike that killed a senior leader of the militant group, the Popular Resistance Committees (PRC), who Israel said had been planning an attack. The PRC has denied that.
The ceasefire deal was brokered by the Egyptian authorities, who reportedly negotiated with each side separately.
Previous deals after earlier rounds of fighting have often proved fragile and taken several days to take settle.