In response to the mortar fire, Israeli tanks and aircraft fired on Hamas positions.
They added that the air force also fired four missiles into an area, south of Gaza city, wounding three Palestinians, before they were rushed to the Shifa Medical, center.
The mortar fire sent off several Code Red sirens in areas of southern Israel near the border with Gaza, though the Israeli military first said the sirens were a false alarm.
According to Brig. Gen. Ronen Manelis, the IDF knows the names of the perpetrators and that they belong to the Palestinian Islamic Jihad, though it still holds Hamas responsible.
The IDF said Thursday evening that Israelis living north of the Gaza Strip can return to their normal lives after a series of strikes in Gaza.
A Reuters witness in Gaza said he saw smoke rising from at least two targets struck by Israel, one belonging to Hamas and another to Islamic Jihad militants.
About a dozen mortar rounds were fired Thursday afternoon at Israeli army forces involved in construction work along the fence that separates Israel from Gaza, according to Lt. Col. Jonathan Conricus, a spokesman for the Israeli military.
An army spokesperson said the attack was carried out by the Hamas and Islamic Jihad terror groups.
Sharp disagreements remained between Palestinian president Mahmud Abbas's Fatah, based in the occupied West Bank, and Hamas, particularly over the fate of public employees in Gaza and security control of the enclave.
In late October, the IDF blew up a tunnel stretching from the Gaza Strip into Israeli territory.
Israel has been developing technology to detect and destroy tunnels since its 2014 war with Hamas, when the group's members used underground warrens to launch attacks and defend themselves from airstrikes.