– Israel's message has been clear. Its red lines reiterated again and again: It does not want to get embroiled in the civil war in Syria.

But, as the fighting draws ever closer to its border and an estimated 11,000 internally displaced civilians have flooded the area, maintaining such a policy might prove challenging.

Forces loyal to Syrian President Bashar Assad are in the midst of a military offensive, aided by Russia, to recapture territory in southern Syria held by rebel groups. The fighting has forced as many as 50,000 people to flee their homes in the Deraa region over the past week, said the United Nations.

Most have headed toward their country's other southern neighbor Jordan, whose border remains closed, but some have turned toward Israel, trying to get as close as they can to the border where the Israeli military keeps a close eye on events and where, according to local media reports, they feel relatively safe.

In a tweet on Friday, Israel's Defense Minister Avigdor Lieberman said the situation was being closely monitored. "We will continue to preserve Israel's security interests and, as always, we are prepared to provide any humanitarian aid to women and children but we will not accept any Syrian refugees into our territory," he wrote.

On Sunday, the Israeli military said it was reinforcing its artillery and armored units in the area in light of what was happening over the border.

Still formally at war with Syria, Israel has waded into the conflict only sporadically, either to curtail Iran's growing influence in the region or when there is spillover from battles taking place along its border. And despite international pleas, Israel has consistently pushed back against taking in refugees, even as neighboring countries such as Lebanon, Jordan and Turkey have accepted Syrian civilians in the hundreds of thousands.

Israel has, however, been active in providing humanitarian aid and medical services to those who arrive at its border. Exactly a year ago, together with international aid agencies, the army established a field hospital on the Golan, part of what it calls "Operation Good Neighbors," though it did work covertly helping before then.

Over the past year, the army says that approximately 6,000 civilians have received treatment and thousands more have visited Israeli hospitals. It has also transferred vast amounts of food, gasoline and essential medical equipment to the population on its border.

Responding to the influx of people arriving in the area last week, the Israeli military said it has increased those efforts. On Friday, it sent hundreds of tents, additional food and other supplies. On Saturday, it had allowed six Syrians, including four children, to cross into Israel for emergency medical treatment.

But for some, Israel's role is not enough. Writing in the Israeli daily Haaretz, former military spokesman Peter Lerner called Lieberman's zero refugee policy "morally questionable."

Professor Moshe Zimmerman, a historian at Hebrew University in Jerusalem, said as long as Syria remained an enemy country, then Israel would not open its gates to refugees from there, but based on "Jewish faith and its past, Israel should have opened the border a long time ago," he said.

The commander of Operation Good Neighbors said it was too early to know what would happen in the coming days or weeks, but said, "I believe that we will continue providing aid for as long as they request our assistance and as long as we can provide it."