The BBC said the government launched the attack as fierce fighting was reported near the historic Old City and the commercial center seized by rebels.
Local Co-ordination Committees reported 20 dead in Aleppo, 13 in a prison revolt, the BBC said. A similar revolt was reported in Homs. Elsewhere 60 deaths were reported.
Three people were hurt attempting to cross from Syria into Iraq when Syrian forces began shelling on the Syrian side at the Boukamal crossing over the Euphrates River. The U.N. refugee agency estimates 10,000 Iraqi refugees have fled Syria in the last week.
Earlier, Israel Radio reported chemical weapons being moved to airports in border areas.
"According to our information, the regime began moving its stocks of weapons of mass destruction several months ago -- with the goal of putting pressure on the region and the international community," a Syrian Free Army statement quoted by Israel Radio said.
The announcement by the rebel group came a day after Syria openly admitted it had chemical weapons and weapons of mass destruction.
Syria's Foreign Ministry accused media outlets of "deliberately taking out of context" statements made by ministry spokesman Jihad Makdissi, who said Syria's WMD will not be used against Syrian civilians, only against foreign invaders.
The state-run Syrian Arab News Agency said the goal of Makdissi's press conference was "to respond to a methodical media campaign" against Syria.
U.S. officials have said Syria, one of eight nations that did not sign the 1992 Chemical Weapons Convention, which outlaws the production, stockpiling and use of chemical weapons, has perhaps the largest stockpile of chemical weapons in the Middle East, including lethal mustard gas and nerve agents, some of which likely have been loaded onto Soviet-type Scud tactical ballistic missiles and artillery shells, The Wall Street Journal reported Tuesday.
U.S. President Barack Obama said Syrian President Bashar Assad's regime would be held accountable if it uses such weapons.
Makdissi rebuffed an Arab League call Monday for Assad to step down in return for "safe passage" for him and his family and for opposition forces to set up a transitional national unity government.
"If the Arab nations who met in Doha [the Qatari capital] were honest about wanting to stop the bloodshed they would have stopped supplying arms and stopped their instigation and propaganda," Makdissi said. "All their statements are hypocritical."
Qatar and Saudi Arabia support the rebels.