There have been intense exchanges of fire between Israeli forces and armed Palestinian militants in Jenin refugee camp, in the occupied West Bank.
The Israeli military began what appears to be one of its most extensive operations in the territory in years with drone strikes early on Monday.
Nine Palestinians have been killed and 100 injured, health officials say.
Israel said it was putting a stop to Jenin being "a refuge for terrorism". Palestinians accused it of a war crime.
The Israeli military said there was no specific timeline for ending the operation, but that it could be "a matter of hours or a few days".
Jenin has become a stronghold of a new generation of Palestinian militants who have become deeply frustrated by the Palestinian Authority's aging leadership and the restrictions of the Israeli occupation.
The city has seen repeated Israeli military raids in the past year as local Palestinians have carried out deadly attacks on Israelis. Other Palestinian attackers have hidden there.
In 2002, during the second Palestinian intifada, Israeli forces launched a full-scale incursion in Jenin. At least 52 Palestinian militants and civilians and 23 Israeli soldiers were killed during 10 days of intense fighting.
Hundreds of Israeli soldiers were still operating inside Jenin on Monday night, more than 20 hours after the operation began.
As well as the hum of drones overhead, regular bursts of gunfire and the loud thuds of explosions came throughout the day from the densely populated refugee camp, which is home to some 18,000 people and is now declared a closed Israeli military zone.
Acrid smoke from burning tyres lit during protests also hung in the air above the city centre. A few young Palestinians were out on the streets, standing close to shuttered shops and staring nervously in the direction of the camp.
The Israeli military has cut off telephone communications and the electricity supply to the camp, making it difficult to get an accurate picture of what is happening. Palestinian medics have also been struggling to reach the dozens of injured there.
At the Palestinian hospital by the main entrance to the camp the mood was grim.
One man told the BBC: "I met my brother's friend. I went up to him and had barely said a few words when he dropped on the ground. I went to run away, then I got hit by two bullets."
Another man said there was a "massacre" in the camp.
"There are children and civilians and they're not letting them out," he added. "Our electricity is cut, they have dug up all our roads. The camp will be destroyed."
Jovana Arsenijevic of the medical charity Médecins Sans Frontières told the BBC she was at a hospital that had seen more than 90 patients wounded by gunfire or shrapnel from explosive devices.
The Israeli military said it was acting on precise intelligence and did not to seek to harm civilians, but many have been caught in the crossfire.
The military allowed about 500 Palestinian families to leave the camp on Monday night. Some raised their hands or waved makeshift white flags in a gesture of surrender.
People told the BBC that some men and teenaged boys had been stopped by soldiers, and kept behind.
The first drone strike overnight targeted an apartment that the military said was being used as a hideout for Palestinians who had attacked Israelis and as a "joint operational command centre" for the Jenin Brigades - a unit made up of different Palestinian militant groups including Hamas and Palestinian Islamic Jihad.
Drones were used for further air strikes and a brigade-size force of troops was deployed in what a military spokesman described as a "counter-terrorism operation" focused on seizing weapons and breaking "the safe haven mindset of the camp, which has become a hornet's nest".
In the past year and a half, Palestinians behind some 50 attacks targeting Israelis have come from Jenin, according to the military.
As armed Palestinians began fighting back from inside the camp, the Jenin Brigades said: "We will fight the occupation [Israeli] forces until the last breath and bullet, and we work together and unified from all factions and military formations."
The Palestinian health ministry said nine Palestinians had been killed by Israeli forces, including three in the overnight drone strike. They all appeared to be young men or in their late teens - some confirmed as belonging to armed groups.
The ministry warned that the death toll might rise because 20 of the injured were in a critical condition.
Another Palestinian was killed by Israeli fire during a related protest near the West Bank city of Ramallah, it added.
The Israeli military said the Palestinians killed in Jenin were affiliated to militant groups.
Troops had also apprehended some 50 militants during the operation, and seized weapons and ammunition, it added.
On Monday evening, Israel's Prime Minister Benjamin Netanyahu praised its forces for entering what he called the "nest of terrorists" and asserted that they were doing so "with minimal injury to civilians".
"We will continue this action as long as necessary in order to restore quiet and security," he added.
There was a furious response to the operation from the Palestinian Authority Prime Minister, Mohammed Shtayyeh.
"What's going on is an attempt to erase the refugee camp completely and displace the residents," he said.
Neighbouring Jordan said the operation was "a clear violation of international humanitarian law", but the US expressed its support for what it called "Israel's security and right to defend its people against Hamas, Palestinian Islamic Jihad, and other terrorist groups".
Israeli Foreign Minister Eli Cohen said the plan was not to expand the military operation outside Jenin, but already Palestinian protests have reached the Hamas-governed Gaza Strip. And the longer this action goes on in Jenin, the greater the risk of another dangerous, wider escalation.
There has been a surge of violence in the West Bank in recent months.
On 20 June, seven Palestinians were killed during an Israeli raid in Jenin which saw the military's first use of an attack helicopter in the West Bank in years.
The next day, two Hamas gunmen shot dead four Israelis near the settlement of Eli, 40km (25 miles) to the south.
A Palestinian man was later shot dead during a rampage by hundreds of settlers in the nearby town of Turmusaya.
That week also saw three Palestinian militants from Jenin killed in a rare Israeli drone strike.
Since the start of the year, more than 140 Palestinians - both militants and civilians - have been killed by Israeli forces or settlers in the occupied West Bank and East Jerusalem, while another 36 have been killed in the Gaza Strip.
Twenty-four Israelis, two foreigners and a Palestinian worker have been killed in attacks or apparent attacks by Palestinians in Israel and the West Bank. All were civilians except one off-duty serving soldier and a member of the Israeli security forces.
BBC
Russia's unmanned Luna-25 spacecraft has crashed into the Moon after spinning out of control, officials say.
Donald Trump has confirmed that he will not take part in Republican presidential debates with his rivals in the race for the White House.