On a visit to the illegal outpost of Evyatar, Mr Ben-Gvir said that "not one or two, but tens and hundreds, and if necessary even thousands," of terrorists should be killed, according to Israeli outlet The Jerusalem Post.
"I give you my full and complete backing, but I want much more from the settlement here, there needs to be a full settlement here, not only here, but in all the hills around us," he added.
"The Land of Israel is for the people of Israel, we are backing you, run to the hills, settle down. We love you."
Mr Ben-Gvir was pictured at the outpost, which is located just outside Nablus in the northern West Bank city of Nablus, the heart of a new generation of Palestinian militancy that is frequently raided by Israeli forces.
Evyatar was established in 2013. Since then, it has been demolished a number of times and is a frequent source of tension between Israel's most radical settlers and the country's military.
During the visit, Mr Ben-Gvir also doubled down on his wish to see a full-scale Israeli military operation in the West Bank, despite warnings from a number of Israeli security experts that such a move would be ineffective and further exacerbate tensions in the region.
The controversial politician, who has faced charges of inciting anti-Arab hate, is under increasing pressure from his far-right base to enact the severe policies that he has advocated throughout his career.
They include a total annexation of the West Bank, widespread legalisation of settlements and the use of the death penalty against those convicted of terrorism.
Israel has the death penalty, but it has only been enacted twice in the nation's history.
On Tuesday, hundreds of settlers, as well as politicians from Mr Ben-Gvir's Religious Zionism party, marched to Evyatar to demand the government recognise the outpost.
The gathering came after a Palestinian gun attack in the West Bank killed four Israelis, just outside the settlement of Eli.
Israeli Prime Minister Benjamin Netanyahu announced soon after that his government would quickly advance the planning of 1,000 new homes in Eli.
Despite his position as National Security Minister, Mr Ben-Gvir was not invited to a government security assessment in the wake of the attack.
Israeli broadcaster Channel 12 quoted unnamed government officials who said he was not present over fears he might leak confidential information. Mr Ben-Gvir was also excluded from similar sessions last month.
His visit to the outpost comes at the end of a week of escalating tensions in the West Bank.
On Monday, seven Palestinians were killed and more than 90 injured in an Israeli raid on the northern West Bank city of Jenin. Eight Israeli troops were also wounded and an Apache helicopter was deployed to protect soldiers who became stranded after a Palestinian explosive disabled an armoured vehicle.
On Tuesday, one Palestinian was killed and homes and vehicles were set alight by Israeli settlers in the town of Turmus Aya.
On Wednesday evening, three people were killed in a rare drone strike near Jenin. The Israeli military said the dead were suspected militants.
Violence between settlers and Palestinians has also taken place, with Israelis vandalising property.