Israel has been attacked by nearly 100 rockets, including 40 in an hour, from Gaza, according to the Israeli army.
Israel has responded with dozens of airstrikes and is continuing to deploy more military resources to the Gaza border.
The Israel Defence Forces (IDF) said close to 100 rockets had been fired at Israel on Monday alone. There are so far no reports of casualties.
Twelve of the rockets were intercepted by rocket defence batteries, the Israeli army said.
Hamas' armed wing, the Ezzedine al-Qassam Brigades, claimed responsibility for the rocket fire.
The bombardment came a few hours after Israel launched 16 airstrikes on targets in Gaza, and followed a night where planes attacked 14 targets, killing at least three people.
Another six died after a tunnel collapsed near the city of Rafah, with Hamas blaming it on an Israeli airstrike - a claim Israel denies.
Israeli army spokesman Lt Col Peter Lerner said two infantry forces were moving to the Gaza border and up to 1,500 reservists were to be mobilised.
Tensions in the region have been inflamed following the kidnap and murder of three Israeli teenagers and the suspected revenge killing of a Palestinian teenager.
Three of the six people arrested over the latter case have reportedly confessed but charges are yet to be brought.
The victim, 16-year-old Mohammed Abu Khadair, was burned alive, according to a preliminary post-mortem examination. He was found in the Jerusalem Forest last week.
Prime minister Benjamin Netanyahu phoned the boy's father to promise that those responsible for the "despicable" murder would be prosecuted, Israeli officials said.
Mohammed's killing followed the murder of Israeli teenagers Gilad Shaar, Naftali Frenkel and Eyal Yifrach.
The three young men were found in shallow graves on June 30, nearly three weeks after they disappeared while hitchhiking home.
Prime minister Netanyahu has blamed Hamas for the murders and warned they "will pay". Hamas has said it was not behind the deaths.