GOLAN HEIGHTS/BEIRUT (Reuters) - Dozens of Syrians approached the Israeli-occupied Golan Heights on Tuesday in an apparent attempt to seek help or sanctuary from a Russian-backed Syrian government offensive, before turning back after a warning from Israel’s army.

Tens of thousands of Syrians have thronged to the Golan in the past month, fleeing a rapidly advancing offensive which has defeated rebels across a swathe of territory near Jordan and Israel and generated pressure on both neighbors to extend aid.

“Go back before something bad happens. If you want us to be able to help you, go back,” an army officer on the Israeli side of a frontier fence, which is partly lined with minefields, told the crowd in Arabic through a megaphone. “Get a move on.”

Explosions sent up smoke a few kilometers (miles) further within Syria, where President Bashar al-Assad’s offensive has triggered the single biggest displacement of the war - several hundred thousand people. Israel has refused to grant asylum to citizens of Syria, with which it is technically at war. But it has admitted thousands of them for medical treatment.

“I think that we have really done all that can be done,” Defence Minister Avigdor Lieberman told Tel Aviv radio station 103 FM. “We are not prepared to accept even one refugee. That’s not our job. There are lots of Arab countries, rich countries.”

Israel captured much of the Golan in 1967 fighting with Syria and annexed the strategic plateau, a move not recognized abroad. Israeli aid, transferred by international humanitarian groups, flows across a 1974 armistice line to a U.N.-monitored buffer zone where many of the refugees are encamped, hoping Assad’s army will steer clear.

TOO CLOSE FOR COMFORT

The Syrians who approached the fence stopped some 200 meters (yards) away. “You are on the border of the State of Israel. Go back, we don’t want to hurt you,” a soldier called out to them.

The crowd, which included women and children, then walked back slowly toward the refugee encampment. Some stopped mid-way and waved white cloths in the direction of the Israeli lines.

An Israeli officer, speaking to Reuters on condition of anonymity, said such processions toward the fence had happened before: “It’s their way of signaling they need new supplies.”

Assad has advanced swiftly, unopposed by his foreign adversaries. The United States, which once armed the southern rebels, told them not to expect it to intervene as the attack got underway last month. The United Nations said last week up to 160,000 Syrians had fled to Quneitra province, some close to the Golan.

Syrian state TV broadcast from al-Haara, a hill captured from rebels on Monday and overlooking the Golan. Government fighters waved rifles and held aloft pictures of Assad as they celebrated. “We will liberate all Syria,” said one of them.

Israel has threatened a harsh response to any attempt by Syrian forces to deploy in the disengagement zone, complicating the offensive as it draws closer. Israel does not want its foes Iran and Hezbollah, both allies of Assad, to form their own Syrian front against it, and has asked Moscow to intervene.

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Russian President Vladimir Putin, speaking alongside U.S. President Donald Trump on Monday, cited the need to restore the Golan to the state that prevailed before the Syrian civil war broke out in 2011.

Hezbollah-controlled al-Manar TV said the Syrian army had captured one of the last rebel-held areas in Deraa province, al-Aliyeh.

At least 14 people were killed when government forces bombarded the nearby village of Ain al-Tineh 10 km (6 miles) from the Golan frontier, the Syrian Observatory for Human Rights reported.