He was a resident of Beit El, an Israeli town north of Jerusalem in the West Bank.
His funeral is scheduled for Wednesday at 4 p.m. at the military cemetery on Mount Herzl in Jerusalem.
"The IDF sends its heartfelt condolences to the family and will continue to support them," said the military.
“We mourn the loss of David Yehudah Yitzchak ... the brave IDF soldier killed in battle. David was raised in Beit-El and was a respected non-commissioned officer in the elite Egoz commando unit. We share in the tremendous grief and send a warm embrace to his family, community, and residents of Beit-El," said Gush Etzion Regional Council Mayor and Yesha Council Chairman Shlomo Ne’eman in a statement.
Sporadic clashes erupted between Palestinian terrorists and Israeli troops into the early hours of Wednesday, with an IDF spokesman saying that the forces would remain "prepared for whatever is required.”
During the initial withdrawal, the military conducted an airstrike targeting gunmen located in a cemetery on the outskirts of Jenin.
The terrorists “posed a threat to security forces as they left the [Jenin] refugee camp,” said the IDF.
The military launched a major counterterror operation in Jenin in the early hours of Monday, including the entry into the city of significant ground forces.
Over 1,000 IDF troops participated in the campaign, which is believed to be the largest deployment in the West Bank in two decades.
The military said on Tuesday its forces had killed 18 Palestinians, all of them terrorists.
Israeli troops arrested well over 100 terror suspects.
During nearly 48 hours of fighting, IDF troops located and demolished at least eight weapon storage sites, six bomb-making labs, three "war rooms," and other terror assets.
The IDF also carried out some 20 drone strikes against various targets.
"I congratulate our courageous fighters who destroyed many terrorist infrastructures in Jenin and thus prevented many terror attacks," Israeli Prime Minister Benjamin Netanyahu said during a visit on Tuesday to the Salem checkpoint, located some 6 miles from Jenin.
"At this moment, we are completing the mission, and I can say our wide-scale operation in Jenin is not a one-time action," he added.
The premier also addressed Tuesday afternoon's terror attack in Tel Aviv, where a Palestinian drove his car into pedestrians at a bus stop on Pinchas Rosen Street in the northeastern Ramat Hahayal neighborhood.
The terrorist, identified as 20-year-old Abed Halilah, then got out of the vehicle and attacked bystanders with a sharp object, police said. There were seven victims in total, one of whom, a pregnant woman, lost her baby as a result of the attack.
Hamas claimed Halilah as a member and praised the attack as a “heroic” response to the military operation in Jenin.
"Whoever thinks that such an attack will deter us from continuing our fight against terrorism is wrong," said Netanyahu.
Israeli Defense Minister Yoav Gallant said on Tuesday that the Jenin operation had restored Israel's freedom to act against terrorist groups throughout the West Bank.
"It will take a little more time until we reach a situation where, as a result of having engaged militarily in Jenin in recent days, we will be able to move anywhere, in the refugee camp or anywhere else, with a team of soldiers, and not with an entire brigade," said Gallant.
The comments echoed those of IDF Chief of Staff Lt. Gen. Herzi Halevi, who earlier on Tuesday said that Israeli forces now "know how to enter where we want, when we need and when we choose."
He added: "There will be no safe place for terrorists—and whoever escaped today, we will make sure to find him tomorrow."
