* Syrian army extends fight for Aleppo
* Rebels say they have forced army to retreat
* Fighters aim to take centre of Syria's biggest city
* Neither rebels nor army control Salaheddine "ghost town"
By Erika Solomon
ALEPPO, Syria, July 31 (Reuters) - Syrian combat aircraft and artillery pounded two areas of Aleppo on Tuesday as the army battled for control of the country's biggest city, but rebel fighters said troops loyal to President Bashar al-Assad had been forced to retreat.
Large clouds of black smoke rose into the sky after attack helicopters turned their machineguns on eastern districts for the first time in the latest fighting and a MiG warplane later strafed the same area.
The battle for Aleppo has become a crucial test for both sides in the 16-month-old rebellion. Neither Assad's forces nor the rag-tag rebels can afford to lose if they hope to prevail in the wider struggle for Syria.
Heavy gunfire echoed round the Salaheddine district in the southwest of the city, scene of some of the worst clashes, with shells raining in for most of the day.
Reuters journalists have established that neither the Syrian army nor rebel fighters are in full control of the quarter, which the government said it had taken at the weekend.
Salaheddine resembled what one journalist called a "ghost town", its shops shuttered, with no sign of life in its apartment buildings and its streets mostly devoid of traffic.
Rebel fighters, some in balaclavas and others with scarves around their faces, fired machine guns and assault rifles around street corners at invisible enemies. Wounded civilians and fighters were carried to makeshift dressing stations.
Syrian state television said on Tuesday troops were still pursuing remaining "terrorists" there -- its usual way of describing rebel fighters.
A rebel commander in Aleppo said his fighters' aim was to push towards the city centre, district by district, a goal he believed they could achieve "within days, not weeks".
The rebels say they now control an arc that covers eastern and southwestern districts.
"The regime has tried for three days to regain Saleheddine, but its attempts have failed and it has suffered heavy losses in human life, weapons and tanks, and it has been forced to withdraw," said Colonel Abdel-Jabbar al-Oqaidi, head of the Joint Military Council, one of several rebel groups in Aleppo.
Oqaidi told Reuters late on Monday more than 3,000 rebel fighters were in Aleppo, but would not give a precise number.
The fighting has proved costly for the 2.5 million residents of Aleppo, a commercial hub that was slow to join the anti-Assad revolt that has rocked the capital, Damascus, and other cities.
While rebels say they will turn Aleppo into the "grave" of the Assad government, thousands of residents have fled and those who remain face shortages of food and fuel and the ever-present risk of injury or death.
"We have hardly any power or water, our wives and kids have left us here to watch the house and have gone somewhere safer," said Jumaa, a 45-year-old construction worker, who complained it was nearly impossible to observe the Muslim fasting month of Ramadan.
"I would say 99.9 percent of the people aren't fasting. How can you fast when you hear mortars and artillery hitting the areas nearby and wondering if you will be next?" he said.
Makeshift clinics in rebel-held areas struggle to deal with dozens of casualties after more than a week of fighting.
Up to 18,000 people have been forced to leave their homes in Aleppo and many frightened residents were seeking shelter in schools, mosques and public buildings, according to figures given by the U.N. refugee agency in Geneva.
The opposition Syrian Observatory for Human Rights said more than 100 people, 73 of them civilians, were killed in Syria on Monday. It said five rebel fighters died during clashes with Syrian forces in Salaheddine.
Rebel fighters, patrolling parts of Aleppo in pick-up trucks flying green-white-and-black "independence" flags, face a daunting task in taking on the well-equipped Syrian army, even if the loyalty of some of its troops is in doubt.
Armed with Kalashnikov assault rifles, machineguns and rocket-propelled grenades they are up against a military that can deploy fighter jets, helicopter gunships, tanks, armoured fighting vehicles, artillery and mortars.
Rebels have captured a small number of tanks and armoured vehicles but they do not seem to have used them in combat yet.
Against a background of divisions among major powers over Syria, U.S. President Barack Obama and Turkish Prime Minister Tayyip Erdogan discussed in a telephone call how they could work together to speed up political transition in Damascus.
"They took up the co-ordination of efforts to accelerate the process of political transition in Syria, including Bashar al-Assad leaving the administration and the meeting of the Syrian people's legitimate demands," Erdogan's office said.
Erdogan, who once enjoyed close ties with Assad, has become one of his fiercest critics and has demanded he step down.
Turkey hosts more than 44,000 Syrian refugees, many of them in border camps where they complain of poor conditions.
Amid growing concern about security on its frontier, Turkey sent at least four heavily armed military convoys to the border with Syria on Monday, although there has been no indication that Turkish forces will cross over.