The Hamas military wing Izzadin al-Qassam and the Ansar al-Quds militant group claimed joint responsibility for the mortar attacks they said were in response to "Zionist crimes." They said one Palestinian was killed and 10 people, including children, were injured Sunday.
The army fired tank shells into southern Gaza.
A statement released by the army said it hit "a number of terror cells and targets of the terrorist organization Hamas in the Gaza Strip in response to the rockets fired this morning toward territory of the state of Israel."
Haaretz said one of the targets hit was a Gaza mosque, which the army said was used by Hamas for "terrorist activities."
Palestinian media reports said five civilians were injured in the Monday military strikes.
Israeli residents living in the Eshkol region were instructed to remain in shelters Monday due to the barrages of mortar shells.
On Sunday in a joint operation conducted by the Israel Security Agency and the army, the air force targeted two terror operatives riding a motorcycle in Rafah, southern Gaza, killing one of them, military officials said.
The army said Tala'at Halil Muhammad Jarbi, 23 a Global Jihad operative, and Abdullah Muhammad Hassan Maqawai, 24, a member of the Ashora Council of the Martyrs of Jerusalem a Gaza-based Global Jihad affiliate, were the targets of the strike. The army said Jarbi was involved in intensive terrorist activities and planned an attack on the security fence on the Israel-Egyptian border in June in which an Israeli civilian construction worker was killed. He was also said to have been plotting another attack on the border with Sinai, the army said.
Jarbi was killed and Maqawai severely injured in the airstrike, the Ma'an News Agency said.