Mrs Netanyahu sent a private letter to Interior Minister Eli Yishai, the main driver in refusing the children permanent status in Israel.
Writing "as a mother to two young boys and a psychologist in the public service", she urged the minister to reconsider his position and allow most of the 400 children to remain in Israel.
The cabinet was split over the issue with ten ministers opposing it and 13 in favour. Interior Minister Yishai, of Shas, opposed along with the other ministers of his party, declaring: "We must not let illegal workers remain and change the identity of the state simply because they have children, it is only an excuse."
But Trade and Industry Minister Binyamin Ben-Eliezer was in favour of allowing all the children to stay and voted against, saying in cabinet: "This is not the state of the Jews as I know it, deporting children."
