The Israeli vehicle held six members of the Lipnick family, from nearby Shavei Shomron.
Ori, 12, was killed at the scene, and her brother Roi, eight, died on the way to Kfar Saba’s Meir Medical Center, according to the Magen David Adom, which responded to the scene along with the IDF.
The driver of the Palestinian vehicle, Fathi Abu Shanab, a 21-year-old university student, was also killed in the collision.
The two children were buried on Wednesday night in Shavei Shomron, and their father, Ohad, left the hospital to attend the funeral.
“God, I do not understand, how could you take two children?” he said.
Earlier in the day Ohad agreed to donate their corneas, which will be transplanted soon to restore the sight of two people.
Ohad’s wife, Shirli, and his oldest son, who was set to celebrate his bar mitzva next month, are in serious condition in Meir Medical Center.
His six-month-old son was lightly injured and is also hospitalized there. A four-year-old son was not in the vehicle at the time of the accident.
According to MDA, another seriously injured Palestinian was airlifted by an IDF helicopter to the Rabin Medical Center in Petah Tikva.
The Red Crescent, which responded to the scene, said Shanab was transported to the Thabet Thabet Hospital.
Police later announced he had died. The Red Crescent also transported three other injured people to An-Najah University Hospital in Nablus, and their condition is between moderate and stable.
Israeli police said that after an initial investigation of the scene, it appeared that the Palestinian driver had been speeding.
Palestinian Authority Police spokesman Louay Arzeikat said Israel denied a request by the PA Police for permission to go to the site of the crash. He added that following fatal car crashes that include Israelis and Palestinians, joint Israeli-Palestinian investigations usually take place.
“It should have been a joint investigation, but they did not give us permission to go there,” he said.
The crash took place in Area C of the West Bank, which is under Israeli security and administrative control.
Red Crescent spokeswoman Erab Fukaha said: “There is usually cooperation between the medical teams on the scene and the two sides [Israel and the Palestinians], in accordance with the professional and humanitarian standards of the Red Cross and Red Crescent.”
PA Civil Affairs Ministry spokesman Walid Wahdan said that the PA and Israeli security officials coordinated the transfer of the critically injured Palestinian to a hospital in Israel.
Wahdan also said that the PA believes that car crashes should always be dealt with from a humanitarian perspective.
“Our view is that this is a matter of saving lives,” he said. “We believe that everything should be done to rescue anyone, irrespective of their religion or nationality.”
In the aftermath of the crash, both Palestinians and Israeli settlers called for Israel to increase traffic enforcement and upgrade the roads in the area.
PA Transportation Minister Muhammad Hamdan said that Israel needs to take greater measures to increase safety on the road where the car accident took place.
“The Israeli occupation authorities need to expand the road where the car crash happened and increase the number of traffic police there,” he said.
According to the spokesman, at least 15 deadly car accidents have taken place on the same road in the past three years, but Israel has taken little action to address safety concerns there.
Samaria Regional Council head Yossi Dagan called on the transportation and public security ministers to immediately create a plan to improve road safety in Judea and Samaria.
Traffic police are particularly lacking, he said.
“We have been working for a long time in order to get additional traffic policemen” and to “increase enforcement on the roads in Samaria. Our many requests were simply not answered,” Dagan said.
Judy Siegel and Adam Rasgon contributed to this report.