Israel's health ministry says at least 545 people have been injured in the Palestinian attacks, according to the Reuters news agency.
At least 22 Israelis have died in the unprecedented attacks, according to emergency services
Thousands of rockets have been fired into Israel from the Gaza Strip in a surprise attack by the Hamas militant group on Saturday morning.
Large plumes of black smoke could be seen rising from a number of Israeli towns.
Israel's defence minister said Hamas had "launched a war" and its troops were "fighting against the enemy at every location".
And footage of Hamas fighters crossing border using paragliders pic.twitter.com/p99GWx7dth— Alistair Bunkall (@AliBunkallSKY) October 7, 2023
Israeli Prime Minister Benjamin Netanyahu said in a statement: "We are at war and we will win."
Mr Netanyahu added: "Our enemy will pay a price the type of which it has never known."
Palestine's President Mahmoud Abbas said the Palestinian people have the right to defend themselves against the "terror of settlers and occupation of troops".
At least 22 people have been killed following the strike according to a local news report that cited the Israeli ambulance service.
About 545 Israelis have been wounded, its health ministry said.
Social media images showed cars on fire and damaged buildings
Phone footage also showed Hamas fighters attempting to reach Israel on small boats, and in a highly unusual development, a number of fighters appeared to have crossed the border using paragliders, reaching the town of Sderot where gun battles were heard.
Footage from security cameras showed them entering the city in pick-up trucks and motorbikes.
Air raid sirens sounded across southern and central Israel, and there were explosions in the cities of Tel Aviv, Ashkelon, Yavne and Kfar Aviv.
A rescue agency said a 70-year-old woman had been critically injured when a rocket hit a building in southern Israel.
Israel said it was attacking targets in the Gaza Strip and the Israel Defense Forces (IDF) warned "the Hamas terror group will pay a very heavy price".
The Israeli military said "a number of terrorists have infiltrated into Israeli territory" and residents along the border were told to stay indoors.
"The military declares a state of war alert," it said in a statement.
Israeli defence minister Yoav Gallant said Hamas had "made a grave mistake this morning and launched a war against the State of Israel".
He added: "IDF troops are fighting against the enemy at every location. I call on all of Israel's citizens to follow security instructions. The State of Israel will win this war."
Several reports have suggested that Hamas kidnapped IDF soldiers with videos circulating on social media appearing to show the captive military troops being paraded on trucks. An IDF spokesman refused to comment on the claims when asked about them.
Prime Minister Benjamin Netanyahu is understood to have convened an emergency meeting of his security cabinet.
A military spokesperson for Israel said Hamas fired 2,500 rockets in Saturday's attack, while the group's military commander Mohammad Deif said 5,000 rockets had been launched.
"This is the day of the greatest battle to end the last occupation on earth," Mr Deif said on Hamas radio.
He said the attack was the beginning of "Operation Al Aqsa Storm" and was in response to Israeli violence in the West Bank, Gaza, and around Al Aqsa mosque compound in Jerusalem.
"Today the people are regaining their revolution," he said in the recorded message.
"We must set the earth on fire under the feet of the occupiers," the militant added.
Palestinian Islamic Jihad militant group said it had joined the attack, while Hamas also called on armed groups in Lebanon to get involved.
Governments around the world have condemned the attacks on Israel.
British PM Rishi Sunak said: "I am shocked by this morning's attacks by Hamas terrorists against Israeli citizens. Israel has an absolute right to defend itself. We're in contact with Israeli authorities, and British nationals in Israel should follow travel advice."
The UK's Foreign Secretary James Cleverly said: "The UK unequivocally condemns the horrific attacks by Hamas on Israeli civilians. The UK will always support Israel's right to defend itself."
Labour leader Sir Keir Starmer "utterly condemn[ed]" the attacks as "an act of terror".
Sir Keir said: "There is no justification for this act of terror which is being perpetrated by those who seek to undermine any chance for future peace in the region."
The attacks come after weeks of heightened tensions along Israel's volatile border with Gaza, and heavy fighting in the Israeli-occupied West Bank.