JERUSALEM — Israel’s message has been clear, its red lines repeatedly emphasized: It does not want to get embroiled in the ongoing civil war in Syria.

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

Forces loyal to President Bashar al-Assad, backed by Russian airstrikes, are in the midst of a final push to recapture territory held by various rebel groups. The United Nations said Monday that 270,000 people have fled their homes to escape bombardments in the nearby province of Daraa, according to the news agency Reuters.

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 Friday, Israeli Defense Minister Avigdor Liberman said the situation was being closely monitored. He offered Israel’s help but stopped short of saying that his country would become a haven for Syrians.

“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 announced it was reinforcing its artillery and armored units in the area in light of what was happening across the border. 

Still formally at war with Syria, Israel has waded into the conflict only sporadically, to curtail Iran’s growing influence in the region or deal with spillover from battles 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 hundreds of thousands of Syrian civilians. 

However, Israel has 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 in the occupied Golan Heights, part of what it calls Operation Good Neighbor, although it did offer covert help before then. 

Over the past year, the army says, approximately 6,000 Syrian 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 Syrian population along Israel’s border.

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

But to some, Israel is not doing enough. Writing in the Israeli daily Haaretz, former military spokesman Peter Lerner called Liberman’s zero-refugee policy “morally questionable.” 

“Israel should make exceptions to its ‘no entry’ policy for refugees, especially orphaned children who are in dire need,” Lerner wrote. And, if Israel will not allow them in, he said, it should at least establish a “safe zone” on the eastern side of the border. 

Moshe Zimmermann, a historian at the Hebrew University of Jerusalem, said that as long as Syria remains an enemy country, Israel will not open its gates to Syrian refugees. But based on “Jewish faith and its past, Israel should have opened the border a long time ago,” he said. 

Zimmermann said Israel has two options in response to the recent developments — open its border or push the international community to create a zone in southern Syria where Israel can bring in medical help and other support for those fleeing the fighting. 

Gal Lusky, founder and chief executive of Israel Flying Aid, a nonprofit that has been instrumental in getting aid from Israel into Syria, said such a zone is essential because “Israel is the only access point to help these people.”

“I don’t think Israel should take in these people, but it should make sure there is a wide-enough buffer zone so they can be safe,” she said. “Women and children are not to blame for this situation, and we need to do what we can now, because I don’t know if we will have access to them in the coming months.”

The commander of Operation Good Neighbor said it was too early to know what would happen in the coming days or weeks as Syrian forces continue their offensive. “It is possible there will be a cease-fire. We need to wait and see,” said the commander, who spoke on the condition of anonymity in accordance with military protocol. “But I believe that we will continue providing aid for as long as they request our assistance and as long as we can provide it.”