The worldwide Israeli news agency Tazpit Press Service (TPS) reported that Islamic Jihad representatives offered compensation to the family for the death of the baby and a woman who may have been her mother.
Israeli military officials announced on Sunday that it launched air strikes to respond to an alleged "Hamas cyber offensive against Israeli targets".
USA president Donald Trump meanwhile assured Israel on Sunday that it had Washington's full support against "these terrorist acts".
The deal is believed to include a number of economic aid and development programmes in Gaza, including providing additional electricity and creating temporary jobs in a territory where unemployment has risen to more than 50%.
Palestinians inspect a damaged bedroom following a late night Israeli missile strike on a building in town of Beit Lahiya, Northern Gaza Strip, Monday, May.
On the Israeli side four civilians were killed as Hamas and Islamic Jihad fired barrages of rockets and at least one anti-tank missile from the enclave, Israeli authorities said.
Israeli officials have said their priority is to confront Iran's attempts to entrench itself militarily on Israel's Syrian border, and don't want to get bogged down in Gaza.
Israel carried out airstrikes against Hamas targets in Gaza, and vowed a tougher crackdown against Islamic terror.
It was a rare admission of a targeted killing by Israel's army, and Netanyahu spoke Monday of having "renewed the policy of eliminating senior terrorists".
The Israeli military said that it had targeted a 34-year-old man who worked in a money exchange office and was responsible for channeling Iranian funds to Hamas and Islamic Jihad.
A spokesman for Hamas, the Islamist movement that runs Gaza, said in response to Netanyahu's statement that although the recent flare-up in violence had come to an end, the wider conflict would continue. Israel will also lighten restrictions on goods brought in through the border crossings with Gaza and extend the Gaza fishing zone back to 15 nautical miles.