The ceasefire came into effect on Thursday after two days of fighting between Israel and militants of the Palestinian Islamic Jihad (PIJ) in Gaza after Israel on Tuesday killed Baha Abu al-Ata, one of the PIJ's most senior commanders in the Gaza Strip, in an airstrike, the BBC reported.
Palestinian media said that missiles hit sites belonging to the PIJ group early on Friday, injuring two people.
In a statement, the Israel Defence Forces (IDF) said the aircraft struck a PIJ compound overnight used to construct missile components, as well as the group's headquarters in the town of Khan Younis.
It said Israel's air defences had intercepted five rockets launched from Gaza since the ceasefire was declared, calling this violation "very severe".
Both sides have warned that they were prepared to retaliate if attacked.
The IDF said it would "continue operating as necessary" to protect Israeli civil, while the military wing of the PIJ said its fighters "still have their fingers on the trigger".
After the death of Abu al-Ata, more than 450 rockets and mortars were fired at Israel, and several waves of airstrikes carried out on Gaza in two days of violence before the ceasefire came into effect, the BBC said.
The fighting left 34 Palestin dead and 111 injured, while 63 Israelis were injured.
Israel said 25 of the Palestin killed were militants, including those hit preparing to launch rockets.
( With inputs from IANS )