The Jihad Jibril Brigades said the mortars targeted the Kissufim military zone northeast Al-Qararra near Khan Younis.
An Israeli military spokeswoman said she had reports of a projectile landing at approximately 7:30 a.m. in the Negev regional council area, north of the Gaza Strip, but said she was not aware of any attacks in the area of Kissufim.
In a statement, the brigades said they would continue to carry out resistance activities against Israeli force occupying Gaza.
Overnight Israeli troops opened fire on a group of Palestinians they said were trying to breach the Gaza Strip border, hitting at least one of them, the military said.
By morning, medics said ambulance crews recovered two bodies killed in the fire, Gaza medical services spokesman Adham Abu Salmiya confirmed.
Israeli forces announced at the time that one was killed and a second injured.
The border shooting came hours after militants fired what were apparently two mortar shells into southern Israel without causing any damage or casualties, the army said.
On Wednesday, Israeli military officials reported two projectile launches from Gaza landing in the Ashkelon region. Neither launch was claimed by a militant group.
The reported projectile launches followed two Israeli airstrikes which hit targets in Gaza overnight, including one smuggling tunnel and a second site in the central Strip.
Israeli military officials said the strikes were in retaliation for earlier projectile launches.