Two Syrian shepherds were exchanged for an Israeli woman under a prisoner exchange deal on Thursday between the Jewish state and Syria mediated by Russia.

Israel's military said the two 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 Damascus' SANA news agency confirmed the swap, identifying the Syrian prisoners as Mohamed Hussein and Tarek al-Obeidan.

Israeli Prime Minister Benjamin Netanyahu later confirmed the exchange was mediated by Russia, which enjoys close ties with the Syrian government and stations soldiers in the country.

Thanking Russian leader Vladimir Putin after the deal, the Israeli PM said he had asked his "friend" to help "and he acted."

Netanyahu said the young Israeli woman -- who had strayed over the border -- was on her way home, and that his country had freed the two shepherds as a gesture of goodwill.

As part of the agreement, he said, a Syrian activist called Nihal al-Mokt currently serving community service would have her sentence shortened by three months.

Earlier, SANA had said the two shepherds were released following a deal conducted through "Russian mediation", that also allowed the release of al-Mokt.

Netanyahu on Tuesday evening had held an emergency cabinet meeting to discuss the "humanitarian" situation in Syria.

Asked to comment Wednesday shortly after SANA reported on the prisoner swap, he called it "a matter of life or death".

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