(CNN) -- A plane full of illegal migrants were flown from Israel back to Africa on Sunday night, the first of what potentially could be thousands of such deportations of people who have illicitly entered the Middle Eastern country in recent years.

Prime Minister Benjamin Netanyahu said at a Cabinet meeting Sunday "the first plane of illegal infiltrators (would) leave for South Sudan" that night, with another aircraft set to depart next week for Africa.

"Today, the government will begin the operation to repatriate illegal work infiltrators to their countries of origin," Netanyahu said, according to a cabinet communique released by Israel´s foreign ministry. "We will do this is an orderly and dignified manner.

The issue of illegal African migrants has been of growing concern in the country in recent months. According to government records, more than 59,000 illegal African immigrants have entered the country in recent years through its southern border with Egypt.

Most of the migrants come from Eritrea, Sudan and South Sudan. Some of them have refugee status and hold temporary permits to remain in the country, but Israel does not recognize the status of most of them and says it is looking for ways to send them back to their home countries.

More than 2,000 new migrants have been reported over the past month.

Some residents of southern Tel Aviv neighborhoods, where there is a large concentration of Africans, have blamed their new neighbors for increasing crime and suffocating the infrastructure and public services. Some also complain the illegal immigration is changing the fabric of Israel.

Earlier this month, an Israeli court approved a government plan to deport 1,500 migrants from Africa. Many Israeli refugee agencies and officials pushed against those plans and called on the government to allow the migrants to stay.

And Israeli authorities announced last Tuesday that they´d detained 240 illegal migrants -- all of them Sudanese -- as part of the controversial plan, with another 300 people volunteering to return to their country of origin.

"We are sending the infiltrators, migrants, back to their homes like all countries in the West, in Europe, in the USA act when dealing with migrants," Interior Minister Eli Yishai said then.

In his remarks Sunday to Cabinet, Netanyahu said that construction of a fence along Israel´s southern border will be finished "in the coming months." Until then, any migrant who is caught crossing the border illegally will be detained "immediately," with Netanyahu noting that "holding facilities" are being built to "to house tens of thousands of infiltrators until they can be sent out of the country."

The prime minister vowed to block such illegal migrants´ entry into Israel and, if they do get in, to "hasten their deportation." He also pointed to a law, recently passed by the Knesset, the boosts fines on those who employ illegal migrants.

Still, while making clear they weren´t welcome in Israel, Netanyahu stressed that they would be treated well.

"We have a Jewish tradition of treating strangers humanely," he said, "And even when we need to deport them from our midst due to the state´s desire to control its borders, we must do so humanely and in a manner that finds expression in a restrained and humane manner." (© 2012 Cable News Network 06/18/12)