"Our people has experienced first-hand the silence of the world and cannot be indifferent in the face of the murder and massacre raging in Syria," Herzog posted on his Facebook page.
Speaking at a panel discussion in Tel Aviv, he called on the government "to act toward receiving refugees from the war in Syria, in addition to the humanitarian efforts it is already making."
There is already hostility in Israel toward asylum-seekers from Africa and a concerted government effort to repatriate them.
Most of those who are not in detention centres live in poor areas on the south side of Tel Aviv, where there have been several protests against them.
Someone identifying himself as Sefi Kamrani wrote on Herzog's Facebook page: "Take all the refugees into your home if you're so worried about them. I'd like to see you live just one week in south Tel Aviv."
Meanwhile, Palestinian president Mahmud Abbas called on the United Nations today to press Israel to allow Palestinians from refugee camps in Syria to take shelter in the Palestinian territories, whose external borders are controlled by the Jewish state.
The UN says there are more than 525,000 Palestinian refugees at its camps in Syria, many of whom have been displaced by the civil war there.
Israel has long been treating wounded Syrians who reach Israeli lines on the occupied Golan Heights, but hostility among the Druze of the area has flared due to rebel attacks on their brethren in Syria.
Previously, Druze in northern Israel's Galilee region stoned a military ambulance they suspected was taking Syrian rebels to hospital.