Boys walk past a fence in the Israeli town of Sderot damaged by an earlier round of rocket fire from Gaza on July 14, 2018.
Throughout the night, wave after wave of alarms sounded in the Hof Ashkelon, Sha'ar Hanegev and Eshkol regions, outside Gaza, sending thousands of Israelis into bomb shelters, where many bedded down for the night with their families.
Palestinian militants fired dozens of rockets into Israel and the Israeli military carried out scores of air strikes as fighting near the Gaza-Israel border intensified overnight into Thursday.
The exchange came amid continued attempts by Egypt to broker a broad cease-fire deal between Israel and Hamas.
Three Israelis were reported wounded in a rocket attack on the southern city of Sderot. Two of those were critically wounded, according to the report.
Rockets fired from Gaza into Israel as seen from Sderot.
They were killed in an airstrike in Jafarawi in central Gaza, the ministry said, while her husband was injured.
Israeli forces said in a statement about 150 rockets were fired from Gaza and at least 25 had been intercepted.
"I made it clear that Gaza will not be linked to Judea and Samaria (the Jewish designation of the West Bank)", Transportation Minister Yisrael Katz told Israel Broadcasting Corporation.
In response, a tank targeted a Hamas position, since Israel holds the organization responsible for all violence coming from Gaza.
United Nations officials have however called for the blockade to be lifted, citing deteriorating humanitarian conditions in the Palestinian enclave run by Islamist movement Hamas where 80 percent of the two million population are dependent on aid.
On Wednesday, an IDF tank again struck Hamas posts in Gaza after gunmen opened fire at a civilian vehicle involved in the construction of a barrier along the border.
Israel halted the supply of petroleum and natural gas to Gaza last week in response to incendiary kites and balloons launched from Gaza into southern Israel.
The IDF closed several roads near the Gaza border earlier on Wednesday after warning it was concerned of a retaliation from Hamas after two of its elite members were killed in an IDF strike on Tuesday.
The demonstrations have been fueled in large part by pervasive despair caused by the blockade that has caused widespread economic hardship and left the coastal territory with crippling fuel shortages and just a few hours of electricity a day.
One Hamas militant was killed in the air strikes, as was a Palestinian woman and her 18 month old child, Palestinian officials said.
A Hamas militant was also killed in one of the strikes, while at least 12 people in Gaza were reportedly injured, health officials said.