Peretz' position was confirmed in a letter from Peretz' chief of staff in response to a request from the acting mayor of Ramat Gan Liad Ilani, which reached Ynet on Sunday.
Ilani, who holds the education portfolio in the Ramat Gan city council, appealed to Peretz, Shas leader Deri and the Director-General of the Population and Migration Authority Prof. Shlomo Mor-Yosef to halt the deportation of Geraldine Esta, a foreign worker from the Philippines, and her children Qian, aged 10, and Catherine aged 5.
The two children were born in Israel and attend school in the city's education system.
The three have been detained at Ben-Gurion Airport since they were arrested at their home last Tuesday.
"The children grew up in the Ramat Gan educational system, where they have studied and made friends," Ilani wrote.
"Their strong integration into the community supports the calls by the parents living in the city to stop the deportation for the good of the children.
"The State of Israel is their home and their homeland, while the mother's country is foreign to them. Under these circumstances, and (as an act of kindness), I ask that you act with urgency to prevent the deportation."
The response from Peretz' office came from Yuval Tzur, the education minister's chief of staff and one of the people closest to him.
In a letter bearing the logo of the office of the education minister, Tzur wrote in reply that while "the matter concerns students in the education system, the law treats the status of foreign nationals in Israel as the exclusive jurisdiction of the interior minister.
Nonetheless, the letter from Tzur also stated that, "Given the sensitivity of the case, it is appropriate for me to ask the interior minister to seriously consider the request (to prevent the deportations), due to the special circumstances involving children who live their lives as part of Israeli society for many years."
Since most of the foreign workers scheduled to be deported by the end of August have kindergarten- and school-age children, Hebrew is their first language and the only country they know, this exception for children born in Israel would essentially mean an end to the entire expulsion campaign.
The deportation operation began last Sunday. Esta and her children were arrested two dats later at their home in Ramat Gan, when the immigration inspectors broke down the door
A hearing was to be held Sunday in Tel Aviv over an appeal filed against the expulsions.
Peretz' position is in contrast to his party's number 2, Bezalel Smotrich, on Sunday reiterated his support for the deportations.