The state news agency Sana accused rebels of blowing up the 11th-Century minaret of the Umayyad Mosque.
However, activists say the minaret was hit by Syrian army tank fire.
The mosque, which is a Unesco world heritage site, has been in rebel hands since earlier this year but the area around it is still contested.
Last October Unesco appealed for the protection of the site, which it described as “one of the most beautiful mosques in the Muslim world”.
Images posted on the internet showed the minaret reduced to a pile of rubble in the mosque’s tiled courtyard.
Other parts of the mosque complex – which dates mostly from the 12th Century – have been badly damaged by gunfire and shell hits.
A report by Sana said fighters from the al-Qaeda-linked Jabhat al-Nusra group had destroyed the once famous landmark.
It quoted an official source saying that “terrorists… placed explosive materials in the minaret and the mosque’s southern door and set them off”.
However, Aleppo-based activist Mohammed al-Khatib, quoted by AP news agency, said a tank shell had “totally destroyed” the 45 m (148 ft) minaret.
The mosque has suffered extensive damage during months of fighting, with antique furnishings and intricately sculpted colonnades affected.
Reports say some ancient artefacts have also been looted, including a box purported to contain a strand of the Prophet Muhammad’s hair.
However, rebels said they had salvaged ancient handwritten Koranic manuscripts and hidden them.
Earlier, rebels and government forces reportedly clashed near Aleppo as they fought for control of a military airbase.
Rebels took a key military position outside the Minnigh airport on Tuesday and launched another raid on Wednesday, according to opposition activists with the Syrian Observatory for Human Rights.
“The rebels, who have laid siege to the airport for months now, entered it for the first time around dawn,” Rami Abdel Rahman, director of the UK-based activist group, told AFP news agency.
Heavy fighting was taking place in the grounds, he added.
Analysts say losing control of the airport would be a strategic blow for the government.
The Free Syrian Army has been trying to seize a number of airbases in the area to disrupt regime supply routes.
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