By Suleiman Al-Khalidi and Tom Perry

AMMAN/BEIRUT (Reuters) - Syrian rebels opened a new front in Aleppo as fighting spread on the third day of a major insurgent counter-attack to break the government's siege of the opposition-held part of the city, and each side accused the other of using poison gas.

The rebels, including both Free Syrian Army factions and jihadists, are seeking to end the siege by seizing government-held areas of Aleppo, in an effort to link the city's rebel-held east with rebel-held rural areas to the west of the city.

Syrian state media said militants had fired shells containing chlorine gas at a residential area of the government-held western part of the city, al-Hamdaniya. Rebels denied that, and said government forces had fired poison gas on another frontline.

State media cited an Aleppo hospital director saying three dozen people - civilians and soldiers - had suffered suffocation in the alleged rebel gas attack, but did not report any deaths.

The Syrian Observatory for Human Rights, a UK-based organization that reports on the war, said it had confirmed reports of suffocation among government fighters in two frontline areas shelled by rebels, but it did not know if chlorine gas was the cause.

The rebels said the army had shelled rebel-held Rashideen district with chlorine and shared videos purportedly showing victims with respiratory problems.

Aleppo, Syria's biggest pre-war city, has become the main stage of conflict between President Bashar al-Assad, backed by Iran, Russia and Shi'ite militias, and Sunni rebels including some supported by Turkey, Gulf monarchies and the United States.

The city has been divided for years between the government-held western sector and the rebel-held east, which the army and its allies put under siege this summer and where they launched a new offensive in September that medics say has killed hundreds.

The Observatory said at least 38 people including 14 children had been killed in rebel shelling of government-held areas of Aleppo in the last 48 hours.

Jaish al Fateh, a rebel alliance including powerful Islamist and jihadist factions, said in a statement they were now moving into a second stage of the offensive after taking several areas with the goal of "ending the siege".

They called on residents of government-held areas in western Aleppo to stay at home or in underground shelters as they spread their offensive, saying they were coming to "liberate" their land. They urged the fighters not to harm anyone who did not carry arms.

Rebels and pro-government sites said most of Sunday's fighting concentrated on the 3000 Apartments housing project in the al-Hamdaniya area. Capturing it would bring the rebels to within several kilometers of the heart of the government-controlled area.

"There are heavy street battles and the regime is now retreating from the area. Its only a matter of time and we will announce its liberation," Abu al Ansari, a fighter from Failaq al Sham, said in a Whatsapp message.

Rebels said the attack had started with preparatory shelling earlier in the day. Russian planes resumed heavy bombing of the rebels' new locations in west Aleppo - the latter also cited on pro-government sites.

There were conflicting accounts of the outcome of the fighting, however, with rebels saying they had taken some buildings in the residential area as they seek to penetrate heavily populated areas under state control.

Rebels said suicide bombers were deployed on the outskirts of the neighborhood, a tactic used on Friday when insurgents seized Dahiyet al-Assad, a cluster of villas once occupied by top army officers covering about a square kilometer on the southwest corner of the city.

The army said it had launched an offensive with allied forces on several fronts in the west and east of Aleppo and recaptured the village of Minian on the western edge of the city, taken at the start of the campaign, and had ambushed rebels who had infiltrated some buildings in Dahiyat al Assad.

Rebels denied that Minian had fallen.

Since launching the large scale assault on Friday, the rebels have deployed numerous suicide car bombs undertaken by radical Islamic groups, including the Turkistan Islamic Party in Syria, a jihadist group operating in Syria.

The rebels' use of scores of car bombs to breach army defense lines has helped them advance. The barrage of hundreds of mortars and missiles fired on the city's western edge from bases in the countryside outside Aleppo has been the most intense bombardment by rebels in recent months.

Fateh al-Sham, a jihadist group formerly known as the Nusra Front, played a big part in a rebel attack in July that succeeded in breaking the government siege on eastern Aleppo for several weeks before it was re-imposed.

The jihadist group earlier released on social media several pictures of the group's leader Abu Mohammad al Golani flanked by military commanders looking over a map with a caption saying "being briefed about the fighting".

(Reporting by Suleiman al Khalidi, Editing by Tom Perry, Clelia Oziel and Alexandra Hudson)