According to reports, the bombs "are in the process of being shipped" and could arrive in Israel in coming weeks.
The US has set up a new program to replace its ageing intercontinental ballistic missiles.
The route is intended to flood the West Bank with weaponry, and by so doing, to eventually make this area a third front in the ongoing long war against Israel.
In the morning, the IDF announced that over the past day, soldiers had located a weapons storage facility also within a school compound in Shejaia.
The FAB-3000 reportedly packs nearly a ton and a half of explosives, according to the Independent. It is a modified munition inspired by early designs used in the Soviet era.
CEO of the ministry Maj.-Gen. (res.) Eyal Zamir signed the acquisition order.
The organization Jamaa Islamiya, a branch of the Muslim Brotherhood in Lebanon, has been involved in several attacks against Israel since the beginning of the war.
Most of the clandestine flow of arms into the country has been bound for the neighboring West Bank, Jordanian officials say.
The Israeli prime minister highlighted Israel's supply of arms as being crucial to its success in defeating Hamas and preventing war with Hezbollah.
Cotton's letter was sparked by Prime Minister Benjamin Netanyahu's accusation that the Biden administration deliberately prevented the shipment of weapons to Israel.