Video footage has shown the aftermath of a barrage of rockets fired from Gaza into Tel Aviv.
Security forces, firefighters and medics can be seen picking their way through the bombed-out remains after a woman was killed in Rishon LeZion, just south of Tel Aviv.
The rocket was a direct hit on the home, setting fire to a car.
The confrontation between Israel and Hamas has been sparked by weeks of tensions in contested Jerusalem.
Violence escalated on Tuesday as Israel launched airstrikes on Gaza while Islamist militants barraged Israel with hundreds of rockets.
The exchange killed a number of militants and civilians in Gaza and at least three people in Israel.
An almost nonstop barrage of rockets from the Gaza Strip and Israeli airstrikes into the territory continued throughout the day in what appeared to be some of the most intense fighting between Israel and Hamas since their 2014 war.
The fire was so relentless that Israel's Iron Dome rocket-defense system seemed to be overwhelmed.
Hamas said it launched a total of 130 rockets, its most intense strike so far, in response to Israel's destruction of a high-rise building in Gaza earlier in the evening.
Since sunset on Monday, 28 Palestinians — including 10 children and a woman— were killed in Gaza, most by airstrikes, health officials there said. The Israeli military said at least 16 of the dead were militants.
Two women were killed by rockets fired from Gaza that hit their homes in the southern city of Ashkelon — the first Israeli deaths in the current violence. At least 10 other Israelis have been wounded since Monday evening.
Israel’s prime minister, Benjamin Netanyahu, has warned the fighting would continue for some time. In a nationally televised speech late Tuesday, he said Hamas and Islamic Jihad "have paid, and will pay, a heavy price."
"This campaign will take time, with determination, unity and strength," he said.
Additional reporting by agencies
