The Yemeni First Armoured Division, led by General Ali Mohsen al-Ahmar, said a major and nine troopers were killed "by treacherous sniping and shelling of the positions of the division," according to a statement released late Sunday.
It accused the elite Republican Guard, led by Saleh's son Ahmed, and other security bodies led by relatives of the veteran leader, as well loyal "thugs" of being behind the killings.
"This was part of the series of crimes committed by Saleh and his bloody gang against peaceful demonstrators and their guards of the soldiers of the free Yemeni army that backs the revolution," added the statement.
The 10 were killed on Saturday and Sunday, as demonstrators camped out for months at Change Square and protected by dissident troops, raised the stakes by marching towards zones of the capital controlled by Saleh's forces, promoting deadly response from loyal troops and gunmen.
On Saturday, Saleh's forces shot dead 12 protesters, while six people, including four demonstrators and two soldiers of Ahmar's division, were killed on Sunday, according to medics. Dozens of others were wounded.
Saba state news agency claimed that three civilians were killed and 12 people, including three soldiers, were wounded Sunday when armed men backing the protesters, including dissident soldiers, opened fire.
Seventeen other people, at least five of them civilians, were killed in clashes which erupted between Saleh loyalists on one side and pro-opposition tribesmen led by Sheikh Sadeq al-Ahmar and dissident army units on the other.
The pro-democracy activists, who have been demonstrating since January to bring an end to Saleh's 33-year rule, had voiced defiance ahead of Sunday's march, saying they would continue to protest regardless of losses.
General Ahmar has called on the international community to take immediate action to stop the bloodshed and force Saleh to step down.
Saleh on Sunday charged the protests of being militarised and part of a coup led by Islamists.
Despite mounting pressure from Western governments as well as the six-nation Gulf Cooperation Council (GCC), Saleh has for months refused to sign the deal, even though he has repeatedly promised that he would.
According to a letter from Yemen's youth movement sent to the United Nations earlier this month, at least 861 people have been killed and 25,000 wounded since mass protests erupted across the country.