As Syrian refugees continued to pour into Europe over the weekend, some Israelis were calling on their government to open the border and allow in those fleeing the ongoing civil war in Syria.

But almost as soon as the discussion started, Prime Minister Benjamin Netanyahu discounted the possibility, saying, "Israel is a small, a very small country that lacks demographic and geographic depth."

Instead, at his weekly cabinet meeting on Sunday, the Israeli leader announced that construction had started on a fence along the country's eastern border with Jordan — a possible pathway for war-weary Syrians to reach Israel but also a way for extremists from groups such as the Islamic State to infiltrate the Jewish state.

"We will not allow Israel to be flooded with illegal migrants and terrorists," Netanyahu said in a statement.

The new barrier will extend from Israel's southern tip up to its existing border fence on the Golan Heights, the spot where Israel touches Syria.

Although Israel is one of five countries bordering Syria and has even seen some spillover from the fighting there, it has not officially taken in any refugees from the mostly Muslim country. The two nations have no diplomatic relations.

Israel has, however, provided medical care for wounded Syrians — about 1,000 or so — who have arrived at its border. It has also indicated that it would assist members of the minority Druze community in Syria, who live near the border with Israel, if their situation deteriorates.

Over the weekend, Israeli opposition leader Isaac Herzog called on the government to follow the lead of some European countries and take in refugees from Syria.

He said Jews could "not remain indifferent to hundreds of thousands of refugees."

Herzog was joined by other political leaders, including Zehava Galon, head of the left-wing Meretz party, who said that the images from Europe were shocking and that taking in a few tens of thousands of refugees not only would not harm Israel, but also would strengthen its standing in the Western world.

Another Knesset Member, Elazar Stern wrote on Facebook that Israel should "grant asylum to a limited number of Syrian refugees and recreate, to a certain degree, (former) prime minister Menachem Begin's first decision, to take in refugees from Vietnam."

Israel is well known for absorbing millions of Jewish immigrants, but it has little experience taking in people from other nations. From 1977 to 1979, Israel provided safe haven to 300 Vietnamese refugees, and in the early 1990s, it accepted 84 Bosnian Muslims from the former Yugoslavia.

However, over the past decade, it has been grappling with the influx of nearly 50,000 asylum-seekers from Africa, mostly Muslims from Sudan and Christians from Eritrea, who arrived by way of Israel's southern border with Egypt.

The presence of thousands of non-Jewish Africans, whom the authorities refer to as infiltrators or migrants, has proved a religious and cultural complication for Israel as it tries to keep the Jewish nature of the state intact.

It has also led to a series of zigzagging policies, including attempting to ban the Africans from seeking employment, internment in a semi-open desert facility and offering to pay them to return to a third country in Africa.

Israeli human rights groups are highly critical of the government's policy toward the Africans, saying they should be fully recognized as asylum-seekers or at least have their status determined. Activists point out that only a handful of people have received official shelter in Israel, a country of just over 8 million.

A parliamentary report published in 2013 noted that since its creation in 1948, Israel has granted official refugee status only to 200 people.