* Biggest rebel assault in inner part of capital in four years
* Rebels hope assault will strengthen hand in peace talks
* Military source says incursion "being dealt with" (Adds rebel assault near Hama)
By Suleiman Al-Khalidi and Tom Perry
AMMAN/BEIRUT, March 21 (Reuters) - Syrian rebels stormed a government-held area in northeastern Damascus on Tuesday for the second time in three days, sources on both sides of the fighting said, in the opposition's first such large scale foray in over four years in the capital.
For rebels, the assault has shown they are still able to wage offensive action, though their situation remains very difficult near Damascus and across the country as a whole.
Separately, an alliance of rebel groups said on Tuesday it had launched a new offensive near the city of Hama in the central part of western Syria.
President Bashar al-Assad and the Syrian army, along with allied Russian, Iranian and Shi'ite militia forces, have gained the upper hand in the war for western Syria over the past 18 months, culminating in the full recapture of Aleppo in December.
Witnesses in Damascus said several rockets were fired into central, government-held parts of the city by rebels and state media reported that the army had conducted numerous air and artillery strikes against insurgents.
The spokesman for one of the main insurgent groups involved in the attack told Reuters new offensive began at 5.00 a.m., targeting an area rebel fighters had seized from government control on Sunday before being forced to retreat.
A Syrian military source told Reuters rebel fighters had entered the area, setting off a car bomb at the start of the attack. The source said a group of rebels that had entered the area had been encircled and were "being dealt with".
The rebel groups have launched the assault from their Eastern Ghouta stronghold to the east of the capital. Government forces have escalated military operations against Eastern Ghouta in recent weeks, seeking to tighten a siege on the area. The rebel assault aims partly to relieve that pressure.
The fighting has focused around the Abassiyin area of the northeastern Jobar district, some 2 km east of the Old City walls, at a major road junction leading into the capital.
A witness in the Tijara residential area near the fighting said dozens of tanks were deployed - an unusual scene for residents of inner Damascus, whose quarters been spared the widespread fighting on the fringes of the sprawling city.
North of Hama, jihadist rebel groups said they had launched a new offensive which the Syrian Observatory for Human Rights, a Britain-based war monitor, said had made a considerable advance and seized points inside the towns of Soran and Maardas.
A military media unit run by Hezbollah said that fighting continued in the towns.
Wael Alwan, spokesman for the Free Syrian Army (FSA) rebel group Failaq al Rahman, said: "We launched the new offensive and we restored all the points we withdrew from on Monday."
He said the attack strengthened the hand of the mainstream opposition ahead of new peace talks in Geneva on Thursday. "Our gains today will give strength to our presence in Geneva after tomorrow," he added.
MESSAGE TO RUSSIA
Another rebel official heading to Geneva said the attack showed the limitations of Russia's extensive military support.
"This is a military and political message to Russia that the regime is weak and has no full control and is unable to decisively tilt the balance in its favour militarily," Issam al Rayess, a spokesman for the FSA's Southern Front alliance of Western and Arab backed rebel groups.
The Syrian military source said: "They entered a narrow pocket - the same area of the (previous) breach - and now this group is being dealt with."
State media said rebels who infiltrated the city and Jobar had fled with scores arrested or killed but gave no details.
State television played what it said was footage taken on Tuesday morning on Faris al-Khouri street, which runs towards the Abbasiyin garages, and showed thick dark smoke rising in the distance.
The government says the attack is being carried out by fighters of the Nusra Front, a jihadist group that was al Qaeda's official affiliate in the Syrian war until it declared they had broken off ties last year. The Nusra Front is now part of an Islamist alliance called Tahrir al-Sham.
The attack has relieved pressure on rebels who have lost ground in the nearby areas of Qaboun and Barza, where the army says rebels have constructed an elaborate network of tunnels that provide essential goods that have for years helped Eastern Ghouta withstand a tough siege.
A rebel commander said the Syrian army was intensifying its shelling on areas where they had advanced in Jobar and towns across Eastern Ghouta. "There is no place that has not been hit," said Abu Abdo a field commander from Failaq al Rahman brigade.
The British-based Syrian Observatory for Human Rights, which monitors the conflict, said at least 143 air raids were conducted by the Syrian army on rebel held eastern parts of Damascus, mostly targeting Jobar, since the rebels launched their offensive.
(Reporting by Suleiman al-Khalidi in Amman, Tom Perry and Angus McDowell in Beirut; Writing by Suleiman Al-Khalidi; Editing by Tom Perry and Alison Williams)