Syria death toll hits nearly 126,000-monitoring group

* Real death toll probably much higher -monitoring group

* More than 6,600 children among dead

* Group appeals for international push to end conflict

By Erika Solomon

BEIRUT, Dec 2 (Reuters) - The death toll in Syria's civil war has risen to at least 125,835, more than a third of them civilians, but the real figure is probably much higher, the Syrian Observatory for Human Rights said on Monday.

The pro-opposition monitoring group also appealed to U.N. Secretary General Ban Ki-moon and "all people in the international community who have a conscience" to increase their efforts to end the 2-1/2 year war.

The conflict began as peaceful protests against four decades of rule by President Bashar al-Assad's family, but under a fierce security force crackdown, turned into an armed insurgency whose sectarian dimensions have echoed across the Middle East.

The Observatory, based in Britain but with a network of activists across Syria, put the number of children killed in the conflict so far at 6,627.

It put the death toll among rebels fighting the Assad government at at least 27,746 rebels, including more than 6,000 categorised as foreign fighters or unknown combatants.

"The number is likely much higher but in many battles, the number of rebels killed is hidden, especially by the (al Qaeda-linked) Nusra Front and Islamic State of Iraq and the Levant," Rami Abdelrahman, head of the Observatory, told Reuters.

He said the observatory had documented 50,430 deaths among the Syrian armed forces and local militias supporting Assad, but said that number too was probably higher.

SECTARIAN CONFLICT

"There are at least 40,000 more dead combatants but they were not included in the toll because the cases were not documented well enough," Abdelrahman said.

Both Sunni and Shi'ite militants from around the region have joined the fight on opposite sides.

Many Sunni Muslim countries support the rebels, who are led by Syria's Sunni majority. Shi'ite Muslim states back Assad, who is from the minority Alawite sect, an offshoot of Shi'ite Islam.

As well as Syrians, nearly 500 Shi'ite foreign militants have died fighting with Assad's army, the Observatory said. Around half of those were from the powerful Lebanese guerrilla group Hezbollah, whose military support for Assad has helped his forces make strategic territorial advances in central Syria.

"The Observatory calls for ... serious efforts (by the international community) to stop the killing in Syria and help its people transition to a democratic state with freedom, justice and equality," it said in a statement.

The United Nations does not give regular casualty counts for Syria. It has said for months that more than 100,000 have died.

International efforts have largely concentrated on a planned peace conference in Geneva next month and on the destruction of Syria's stockpile of chemical weapons.

The West blames Assad for a poison gas attack near Damascus on Aug. 21 that killed hundreds of people, but are now working with his forces to remove and destroy such weapons from Syria.

However, regular combat continues, including daily air strikes. The Observatory, which gives daily death tolls in Syria as well, usually cites more than 100 people killed each day, although the death toll in recent days has been double that.

"They should not just be concerned with destroying chemical weapons when tens of thousands of Syrians have been killed by all kinds of weapons since the poison gas attacks of Damascus," the group said. (Editing by Gareth Jones)