BEIRUT (Reuters) - Abu Ahmad has sheltered at the frontier of the Israeli-occupied Golan Heights for days, fleeing an army offensive that has swept through southwestern Syria.

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His family has already moved twice since the assault started in late June, and he worries the battles will creep toward them again. Now, they have nowhere left to go.

“We aren’t even able to sleep more than a few hours, because of intense fear that the regime will attack us here,” Abu Ahmad, 58, told Reuters.

The farmer, living with his wife and two children in a field among makeshift tents, are among thousands of Syrians who sought refuge at the Golan frontier.

In three weeks, Syrian government forces have seized swathes of Deraa province from insurgents in the south with the help of Russian air power. The offensive is expected to turn next to rebel parts of Quneitra province near the Golan, which Israel took from Syria in the 1967 Middle East war.

The United Nations says the fighting has uprooted more than 320,000 people, most sheltering at the frontiers, in the biggest exodus of the seven-year war. Both neighbors Israel and Jordan said they would not let refugees in and have distributed aid inside Syria.

The Damascus government says it only targets militants and wants to end their rule so that Syrians can go home.

Abu Ahmad said he did not want to return to his village of Kheil in Deraa province now that it had come back under state rule. But he does not know what his family will do.

“There is no trust in this regime,” said Abu Ahmad, who has lost a daughter to shelling and a son to sniper bullets. “We are scared for our children and ourselves.”

He also believed they would not be safe going to remaining insurgent territory in northern Syria if there was an evacuation deal, because it could be the army’s next target. He said he would not mind escaping to Israel if that was possible.

Israel has refused to accept refugees from the multi-sided conflict in Syria, a country with which it remains officially in a state of war - though it has taken in several thousand Syrians for medical treatment since 2011.

Waves of people in south Syria have moved again in recent days after some Deraa rebels surrendered in a Russian-brokered ceasefire.

Abu Ahmad’s family ran from Kheil around two weeks ago when a missile hit near their home and their neighbor’s house collapsed. “The warplanes turned (the village) into a pile of rubble,” he added.

First, they went to the border fence with Jordan, but authorities refused to let them in as refugees, he said.

They fled again further west toward the Golan frontier, as government forces advanced along the Jordanian border, later seizing it entirely.

If the army marched on toward him, Abu Ahmad said there was nothing he could do. “It’s up to God.”