Israel says its jets have hit two targets in the Gaza Strip.
The Israeli military said the targets were Hamas weapon manufacturing facilities, adding that the strikes were in response to two rockets fired from Gaza into southern Israel.
A pregnant woman and her young daughter in a nearby house were killed, Palestinian officials said.
In the West Bank, Israeli police say a Palestinian woman set off an explosive device at a checkpoint.
She was stopped by police while driving on Sunday morning near the Israeli settlement of Maale Adumim.
She "shouted 'Allahu Akbar' (God is great) and detonated an explosive device", a police spokeswoman said, adding that the woman was in critical condition and a policeman was slightly wounded.
Initial reports had said the woman had died in the blast.
Following Sunday's air strikes, Israel Defense Forces' spokesman Lt Col Peter Lerner said: "The IDF holds Hamas responsible for any act of aggression from the Gaza Strip."
As well as the two reported deaths, medical staff in the Zeitun sector south of Gaza City say three people are trapped in the rubble of the destroyed house.