A spokesperson with the ministry confirmed to Xinhua that Defense Minister Benny Gantz has authorized the delivery of the vaccines.
The Jewish state has launched an aggressive coronavirus vaccine campaign on Israeli territory, an effort widely regarded as the world's fastest per capita.
"Israeli authorities must ensure that vaccines are equally provided to the Palestinians living under their control, in order to meet their obligations under worldwide law".
This is according to the Palestinian prisoners' affairs commission that accused the Israeli prison administration of depriving the Palestinian inmates of medical care. The rest of an expected 5,000 doses will be sent in three more shipments.
Hundreds of Palestinians work in Israel without a permit and often police chase them and detain them before sending them back to the occupied West Bank where work is more scarce than in Israel and pay is much less.
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The COVID-19 vaccine roll-out plan so far, Amnesty had noted at the time, "excludes the almost 5 million Palestinians who live in the West Bank and Gaza Strip, under Israeli military occupation".
Israel has emerged as a world leader in vaccinating its citizens. There are about 2.7 million Palestinians residing in the West Bank, and another 1.8 million in Gaza.
The PA announced this month that it had signed four contracts to obtain vaccines against the virus, which will be delivered in the coming months and cover 70 percent of the Palestinian population.
Global human rights groups and United Nations experts have said Israel is responsible for the wellbeing of Palestinians in these areas.
On Friday, five Israeli Occupation human rights organizations resorted to the Israeli Supreme Court demanding the vaccination of Palestinian prisoners, saying that this matter is a "legal and moral duty".