In a rare public statement, Mohammed Deif said 5000 rockets had been fired into Israel early on Saturday to begin Operation Al-Aqsa Storm.
Israel also reported an infiltration from Gaza.
"We've decided to say enough is enough," Deif said as he urged all Palestinians to confront Israel.
Deif, who has survived multiple Israeli assassination attempts, does not make public appearances.
His message was delivered in a recording.
The Israeli military said it was striking targets in the Gaza Strip as air raid sirens sounded in Jerusalem.
The sounds of at least three explosions could be heard as Israel deployed anti-rocket defences.
The attack on Jerusalem is considered a major escalation by Israel.
The Israeli military said "a number of terrorists have infiltrated into Israeli territory".
The latest rocket launches follow weeks of heightened tensions along Israel's border with Gaza.
It gave no further details, but amateur videos posted on social media showed what appeared to be uniformed gunmen inside the Israeli border town of Sderot.
The sound of gunfire could be heard in the videos, whose authenticity could not immediately be verified.
The sound of outgoing rockets whooshing through the air could be heard in Gaza on Saturday and sirens wailed as far away as Tel Aviv, some 70km to the north, during an early morning barrage that lasted more than 30 minutes.
Israel's Magen David Adom rescue agency said a 70-year-old woman was critically injured when a rocket hit a building in southern Israel.
Elsewhere, a 20-year-old man was moderately injured by rocket shrapnel, it said.
As the rocket attacks continued throughout southern and central Israel, millions of Israelis were instructed to stay near bomb shelters in their homes and apartment buildings.
The army said residents next to Gaza should stay in their homes due to the "security incident".
Palestinian media in Gaza reported a possible attempt by militants to infiltrate Israel, but no further details were immediately known.
The launches came after weeks of heightened tensions along Israel's volatile border with Gaza, and heavy fighting in the Israeli-occupied West Bank.
Israel has maintained a blockade over Gaza since Hamas, an Islamic militant group that opposes Israel, seized control of the territory in 2007.
The bitter enemies have fought four wars since then.
Palestinian attacks on Israeli targets have killed more than 30 people so far this year.
There have also been numerous rounds of smaller fighting between Israel and Hamas and other smaller militant groups based in Gaza.
The blockade, which restricts the movement of people and goods in and out of Gaza, has devastated the territory's economy.
Israel says the blockade is needed to keep militant groups from building up their arsenals.
The Palestinians say the closure amounts to collective punishment.
The rocket fire comes during a period of heavy fighting in the West Bank, where almost 200 Palestinians have been killed in Israeli military raids this year.
Israel says the raids are aimed at militants, but stone-throwing protesters and people uninvolved in the violence have also been killed.
Palestinian attacks on Israeli targets have killed more than 30 people.
The tensions have also spread to Gaza, where Hamas-linked activists held violent demonstrations along the Israeli border in recent weeks.
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