Retaliatory rocket fire by the rebels on government-held western areas of the city has killed 55 civilians, the monitor says
The government assault on the northern city has spurred a mass exodus of tens of thousands of residents from the opposition-held east and prompted fresh calls by Russia for aid corridors.
President Bashar al-Assad's forces captured the city's northeast this week and were focused on seizing Sheikh Saeed, a large district on the city's southeast edges.
But anti-government fighters put up a strong defence there overnight, rolling back recent government gains, according to the Syrian Observatory for Human Rights.
"The regime and allied fighters... wanted to take this neighbourhood at any cost, because capturing it would allow them to target all remaining rebel-held districts," said Observatory head Rami Abdel Rahman.
"But rebels put up ferocious resistance, because they knew they would be trapped if Sheikh Saeed fell," Abdel Rahman added.
The head of the Britain-based monitor said opposition forces were now once again in control of at least 70 percent of the neighbourhood.
Sheikh Saeed borders the last remaining sections of Aleppo still in rebel hands -- a collection of densely populated residential neighbourhoods where thousands have sought refuge from advancing regime forces.
In preparation for street-by-street fighting in these districts, hundreds of fighters from Syria's elite Republican Guard and Fourth Division arrived in Aleppo on Friday, according to the Observatory.
More than 300 civilians, including dozens of children, have been killed in east Aleppo since the government began its offensive on November 15, according to the Observatory.
Retaliatory rocket fire by the rebels on government-held western areas of the city has killed 55 civilians, the monitor says.
According to Syrian state news agency SANA, one civilian was killed and three were wounded Friday in rebel rocket attacks.
An AFP correspondent could hear steady rocket fire on west Aleppo overnight and into Friday morning.
Intermittent clashes on Friday rocked a block of residential buildings on the city's eastern edges, where advancing regime forces have sought to secure the road leading towards Aleppo's airport.
The escalation of violence in Aleppo has been met with international outrage, including a warning by the UN that the city's east could become "a giant graveyard."
Russia on Thursday proposed setting up four humanitarian corridors into east Aleppo to bring in aid and evacuated severely wounded people.
Moscow has announced several humanitarian pauses in Aleppo to allow civilians to flee, but until the recent military escalation, only a handful did so.
Its support for Assad, including launching a bombing campaign in support of his forces in September 2015, means many residents of east Aleppo have been wary of such offers in the past.
Since Saturday more than 50,000 people have poured out of east Aleppo into territory controlled by government forces or local Kurdish authorities, according to the Observatory.
Many are transported to temporary shelters outside the city, where they register with Syrian authorities to receive food, blankets, and mattresses.
For many, the hot meals they receive at these shelters are their first in months, after a suffocating regime siege since July on Aleppo's rebel-held districts.
The loss of east Aleppo -- a rebel stronghold since 2012 -- would be the biggest blow to Syria's opposition in more than five years.
More than 200 civil society groups on Thursday appealed to the UN's General Assembly to take action on Syria's five-year war because "there is no sign that the Security Council deadlock will end anytime soon."
"This is why we, a global coalition of 223 civil society organisations, urgently call upon UN member states to step in and request an Emergency Special Session of the UN General Assembly to demand an end to all unlawful attacks in Aleppo and elsewhere in Syria, and immediate and unhindered humanitarian access so that life-saving aid can reach all those in need."
Syria's conflict erupted in March 2011 with protests calling for Assad's ouster, but it has since evolved into a bloody and highly globalised war.
The violence has killed more than 300,000 people and forced more than half the country's pre-war population out of their homes.