BEIRUT, Dec 18 (Reuters) - Syrian rebels took full control of the Yarmouk Palestinian refugee camp on Monday after fighting raged for days in the district on the southern edge of President Bashar al-Assad's Damascus powerbase, rebel and Palestinian sources said.

The battle had pitted rebels, backed by some Palestinians, against Palestinian fighters of the pro-Assad Popular Front for the Liberation of Palestine-General Command (PFLP-GC). Many PFLP-GC fighters defected to the rebel side and their leader Ahmed Jibril left the camp two days ago, rebel sources said.

"All of the camp is under the control of the (rebel) Free Syrian Army," said a Palestinian activist in Yarmouk. He said clashes had stopped and the remaining PFLP fighters retreated to join Assad's forces massed on the northern edge of the camp.

The battle in Yarmouk is one of a series of conflicts on the southern fringes of Assad's capital, as rebels try to choke the power of the 47-year-old leader after a 21-month-old uprising in which 40,000 people have been killed.

Government forces have used jets and artillery to try to dislodge the fighters but the violence has crept into the heart of the city and activists say rebels overran three army stations in a new offensive in the central province of Hama on Monday.

On the border with Lebanon, hundreds of Palestinian families fled across the frontier following the weekend violence in Yarmouk, a Reuters witness said.

Syria hosts half a million Palestinian refugees, most living in Yarmouk, descendants of those admitted after the creation of Israel in 1948, and has always cast itself as a champion of the Palestinian struggle, sponsoring several guerrilla factions.

Both Assad's government and the mainly Sunni Muslim Syrian rebels have enlisted and armed divided Palestinian factions as the uprising has developed into a civil war.

"NEITHER SIDE CAN WIN"

Syrian Vice President Farouq al-Sharaa said in a newspaper interview published on Monday that neither Assad's forces nor rebels seeking to overthrow him can win the war.

Sharaa, a Sunni Muslim in a power structure dominated by Assad's Alawite minority, has rarely been seen since the revolt erupted in March 2011 and is not part of the president's inner circle directing the fight against Sunni rebels. But he is the most prominent figure to say in public that Assad will not win.

Sharaa said the situation in Syria was deteriorating and a "historic settlement" was needed to end the conflict, involving regional powers and the U.N. Security Council and the formation of a national unity government "with broad powers".

"With every passing day the political and military solutions are becoming more distant. We should be in a position defending the existence of Syria. We are not in a battle for an individual or a regime," Sharaa was quoted as telling Al-Akhbar newspaper.

"The opposition cannot decisively settle the battle and what the security forces and army units are doing will not achieve a decisive settlement," he said, adding that insurgents fighting to topple Syria's leadership could plunge it into "anarchy and an unending spiral of violence".

Sources close to the Syrian government say Sharaa had pushed for dialogue with the opposition and objected to the military response to an uprising that began peacefully.

In a veiled criticism of the crackdown, he said there was a difference between the state's duty to provide security to its citizens, and "pursuing a security solution to the crisis".

He said even Assad could not be certain where events in Syria were leading, but that anyone who met him would hear that "this is a long struggle...and he does not hide his desire to settle matters militarily to reach a final solution."

In Hama province, rebels and the army clashed in a new campaign launched on Sunday by rebels to block off the country's north, activists said.

The Syrian Observatory for Human Rights, an opposition-linked violence monitor, said fighting raged through the provincial towns of Karnaz, Kafar Weeta, Halfayeh and Mahardeh.

It said there were no clashes reported in Hama city, which lies on the main north-south highway connecting the capital with Aleppo, Syria's second city.

Qassem Saadeddine, a member of the newly established rebel military command, said on Sunday fighters had been ordered to surround and attack army positions across the province. He said Assad's forces were given 48 hours to surrender or be killed.

In 1982 Hafez al-Assad, father of the current ruler, crushed an uprising in Hama city, killing up to 30,000 civilians.

Qatiba al-Naasan, a rebel from Hama, said the offensive would bring retaliatory air strikes from the government but that the situation is "already getting miserable".