Syrian government forces have used helicopter gunships and artillery against rebels in Aleppo, the country's largest city, amid growing concern for the situation of the civilian population there.
Rebel fighters, however, said troops loyal to President Bashar al-Assad had been forced to retreat from key areas of the city.
Syrian state television said on July 31 troops were still pursuing remaining "terrorists" there -- the usual way of describing rebel fighters.
A rebel commander in Aleppo said his fighters' aim was to push toward the city center, district by district, a goal he believed could be achieved "within days, not weeks."
The rebels say they now control an area that covers eastern and southwestern districts of the city, but their claim could not be independently confirmed.
The battle for Aleppo, a city of more than 2 million, has become a crucial test for both sides in the 16-month-old rebellion.
The United Nations, meanwhile, says that thousands of residents have fled the city or taken refuge in safer areas.
The UN's refugee agency says there are some 18,000 people displaced within the city.
UN High Commissioner for Refugees spokeswoman, Melissa Fleming, expressed concern over the refugee problem, adding that "thousands of frightened residents are seeking shelter in schools, mosques, and public buildings. These are the people who haven't fled the city."
Fleming praised Iraq for accepting Syrian refugees, saying that ''we have over 11,000 now who've sought refuge in Iraq, and we are grateful for the assurances from the Iraqi government that the border will remain open to Syrians fleeing the violence.''
But there are much more refugees, about 44,000, in Turkey and there are concerns that the offensive by Assad's army in Aleppo could lead to increasing numbers.
Early on July 31, Turkish media reported that Turkish Prime Minister Recep Tayyip Erdogan and U.S. President Barack Obama discussed the situation in Syria during a phone call.
The phone call took place on July 30 and Turkish media reported that Erdogan and Obama spoke for about 30 minutes.
The White House said the United States and Turkey have agreed to step up efforts to achieve "political transition" in Syria, including the departure of Assad.
A statement from Erdogan's office said that among other things the two leaders "agreed on the coordination of efforts to help Syrians forced to flee to Turkey and neighboring countries."
With reporting by AP, dpa, Reuters, and BBC