Gunmen from the Palestinian Hamas group appeared to have infiltrated Israel in an attack which also included intense rocket fire from the Gaza Strip.
Video shows the aftermath of the strikes and warning sirens across the south and center of the country, including in Jerusalem.
Social-media footage appeared to show clashes in the streets and gunmen in Jeeps roaming the countryside. Palestinian media reported that fighters had taken some Israelis captive, and Hamas media circulated video footage apparently showing a destroyed Israeli tank.
In a video address, Israeli Prime Minister Benjamin Netanyahu said "citizens of Israel. We are at war, not an operation, not an escalation, a war."
One Israeli woman was killed, according to Israeli emergency services, as ambulance crews were deployed around the Gaza Strip where Israel's military said it was operating, without giving further details, Reuters reported.
Israel's Prime Minister Benjamin Netanyahu called an emergency meeting of security officials, and Israel's military said it was on a war footing. Newsweek has contacted the IDF for comment.
A rocket fired from Gaza has struck a residential area in Israel. pic.twitter.com/mHODxDVCHu
— Joe Truzman (@JoeTruzman) October 7, 2023
Ashkelon in southern Israel just now, after direct hit by a Hamas rocket from Gaza! pic.twitter.com/R0dGvypZQC
— Arsen Ostrovsky (@Ostrov_A) October 7, 2023
Hamas claims to have fired 5,000 rockets towards Israel over the course of two hours
— i24NEWS English (@i24NEWS_EN) October 7, 2023
Multiple points of impact reported across the country pic.twitter.com/4Q435F0ono
Hamas military commander Mohammad Deif has called on Palestinians everywhere to fight and there were reports of gunbattles between Palestinian fighters and security forces in the the most serious escalation since Israel and Hamas fought a 10-day war in 2021. He said that 5,000 rockets had been launched in what he described as "the day of the greatest battle to end the last occupation on Earth."
The Israeli military said its forces were operating inside Gaza and that residents in the area surrounding the Gaza Strip had been told to stay in their homes.
There were reports of armed clashes along the separation fence with Israel, near the southern town of Khan Yunis, and the Palestinian Islamic Jihad group said its fighters were joining Hamas.
Israel's defence minister Yoav Gallant said Hamas had launched a war against Israel and "has made a grave mistake." He added that Israel Defense Forces (IDF) troops were "fighting against the enemy at every location" and "the State of Israel will win," the BBC reported. The IDF said it was striking Hamas targets in Gaza.
"Israel is under attack," wrote the country's ambassador to the United States and retired IDF Brigadier General Michael Herzog on X (formerly Twitter).
"This offensive was launched while Israelis were celebrating a religious Jewish holiday," Herzog wrote, adding that it "cannot and will not go unanswered, and we expect the free world to unequivocally condemn it and support Israel's right to self defense."

Update 07/10/23, 4 a.m. ET: This article has been updated with further information.
Update 07/10/23, 6:51 a.m. ET: This article has been updated with the quote from the Israeli Prime Minister Benjamin Netanyahu.