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Israel's military said the two shepherds had been arrested "a few weeks" ago, after they crossed the contested border in the Israeli-occupied Golan Heights.

The army "returned (the) two shepherds to (the International Committee of the) Red Cross representatives through the Quneitra Crossing, in accordance with an Israeli Government directive," it said in a statement.

The military gave no further details on the identity of the men, but Syria's SANA news agency confirmed the swap, identifying the "Syrian prisoners" as Mohamed Hussein and Tarek Al-Obeidan.

SANA said the pair were released following a deal conducted through "Russian mediation", that also allowed the release of Syrian woman activist Nihal Al-Mokt, in exchange for a young Israeli woman who had strayed into Syria.

Israeli Prime Minister Benjamin Netanyahu on Tuesday evening held an emergency cabinet meeting to discuss the "humanitarian" situation in Syria.

Asked on Wednesday shortly after the SANA report of a prisoner swap, Netanyahu said it "was a matter of life or death".

Netanyahu, in an interview with Israeli military radio, called it a "sensitive" matter.

"I am using my personal contacts with President (Vladimir) Putin to resolve the problem," Netanyahu told the radio station.

Israel seized much of the Golan Heights from Syria in the Six-Day War of 1967 and later annexed it in a move not recognised by the international community.

The countries remain technically at war.

Israel routinely carries out air strikes in Syria, mostly against targets linked to Iran, in what it says is a bid to prevent its arch foe from consolidating a foothold on its northern border.

Agencies contributed to this report.