* Rebels take control of Palestinian district of Damascus
* Yarmouk area could serve as base for assault on capital
* No signs of Assad on verge of overthrow - Iran
* Hundreds of Palestinian families flee to Lebanon
BEIRUT, Dec 18 (Reuters) - Russia sent warships to the Mediterranean to prepare a potential evacuation of its citizens from Syria, a Russian news agency said on Tuesday, a sign President Bashar al-Assad's key ally is worried about rebel advances now threatening even the capital.
Moscow acted a day after insurgents waging a 21-month-old uprising obtained a possible springboard for a thrust into Damascus by seizing the Yarmouk Palestinian camp, an urban zone just 2 miles (3 km) from the heart of the city, activists said.
The Syrian opposition has scored significant military and diplomatic gains in recent weeks, capturing several army installations across Syria and securing formal recognition from Western and Arab states for its new coalition.
Despite those rebel successes, bloodshed has been rising with more than 40,000 killed in a movement that began as peaceful street protests but has transformed into civil war.
Assad's pivotal allies have largely stood behind him and Iran, believed to be his main bankroller in the conflict, said there were no signs of Assad was on the verge of being toppled.
"The Syrian army and the state machine are working smoothly," Deputy Foreign Minister Hossein Amir-Abdollahian said in Moscow on Tuesday.
But Russia, Assad's primary arms supplier, has appeared to waver with contradictory statements over the past week stressing opposition to Assad stepping down and airing concerns about a possible rebel victory.
Russia's Interfax news agency quoted unnamed naval sources on Tuesday as saying that two armed landing craft, a tanker and an escort vessel had left a Baltic port for the Mediterranean Sea. Russia has a naval maintenance base in the Syrian port of Tartus, around 250 km (155 miles) northwest of Damascus.
"They are heading to the Syrian coast to assist in a possible evacuation of Russian citizens ... Preparations for the deployment were carried out in a hurry and were heavily classified," the Russian agency quoted the source as saying.
Assad and his minority Alawite sect retain a solid grip on most of the coastal provinces of Tartus and Latakia, where their numbers are high. But the mostly Sunni Muslim rebels now control wide swathes of rural Syria, have seized border zones near Turkey in the north and Iraq to the east, and are pushing hard to advance on Damascus, Assad's fulcrum of power that sits close to the western frontier with Lebanon.
It was not possible to independently verify the Interfax report, which came a day after Russia confirmed that two citizens working in the Latakia province were kidnapped along with an Italian citizen. About 5,3000 Russian citizens are registered with consular authorities in Syria.
YARMOUK A "RED LINE"
In Damascus, activists reported overnight explosions and early morning sniper fire around the Palestinian refugee camp of Yarmouk. The Yarmouk and Palestine refugee "camps" are actually densely populated urban districts home to thousands of impoverished Palestinian refugees and Syrians.
"The rebels control the camp but army forces are gathering in the Palestine camp and snipers can fire in on the southern parts of Yarmouk," rebel spokesman Abu Nidal said by Skype.
"Strategically, this site is very important because it is one of the best doors into central Damascus. The regime normally does not fight to regain areas captured any more because its forces have been drained. But I think they could see Yarmouk as a red line and fight back fiercely."
Syria hosts half a million Palestinian refugees, most living in Yarmouk, descendants of those admitted after the creation of Israel in 1948. Damascus has always cast itself as a champion of the Palestinian struggle, sponsoring several guerrilla factions.
The battle in Yarmouk was one of a series of conflicts on the southern edges of Damascus, as the rebels try to seal off the capital in their campaign to end 42 years of rule over the major Arab state by the Assad family.
Both Assad's government and the rebels have enlisted and armed divided Palestinian factions.
Streams of refugees have fled Yarmouk. Many have headed to central Damascus while hundreds more have crossed into Lebanon.
"We walked out on foot without our belongings until we reached central Damascus. We got in a taxi and drove straight for the border," said 75-year-old Abu Ali, speaking at the Lebanon's Masnaa border crossing.
Abu Ali said around 70 percent of Yarmouk residents had fled and many had slept rough on the streets of Damascus.
MEDICAL SHORTAGES, EXTREME HUNGER
Around 200 people died in Syria on Monday alone, according to the British-based Syrian Observatory for Human Rights, which has a network of activists across the nation. Violence has risen sharply, and with it humanitarian conditions are deteriorating.
The World Health Organisation said around 100 people were being admitted daily to the main hospital of Damascus and that supplies of medicines and anaesthetics were scarce.
It also reported a rise in cases of extreme hunger and malnutrition coming from across Syria, including the insurgent-dominated rural areas outside the capital, where Assad has unleashed warplanes to try to dislodge rebel units.
Aid organisations say fighting has blocked their access into many conflict zones, and residents in rebel-held areas in particular have grappled with severe food and medical shortages.
Fighting raged across Syria on Tuesday, with fighter jets and ground rockets bombarding rebel-controlled eastern suburbs of the capital and army forces shelling a town in Hama province after clashes reignited there over the weekend.
The Syrian government severely restricts media access into the country, making it difficult to report events on the ground.
An news team for the American NBC network who were kidnapped after entering Syria through the rebel-held northern border returned to Turkey on Tuesday after being freed in a gunfight.
NBC chief foreign correspondent Richard Engel said his team was held by an unidentified band for five days, and the men were subjected to psychological torture including mock shootings.
He said he had a "very good idea" who his captors were.
"This was a group known as the shabbiha. This is a government militia. These are people who are loyal to President Bashar Assad," he said on NBC, adding that the kidnappers spoke openly about their allegiance to the Damascus government.