Those killed were part of a convoy carrying some 600 detainees heading to Abu Zaabal prison in northern Egypt, according to reports.
Detainees in one of the lorries managed to capture a police officer inside and reports claim security forces fired tear gas into it in the hope of freeing the badly beaten officer.
Officials said those killed, died from suffocation.
However, their version of events contradicted reports about the incident carried by state media.
The website of Egyptian state television reported that the deaths took place after security forces clashed with militants near the prison and detainees came under fire while trying to escape.
State media also said all those killed and the gunmen belonged to the Muslim Brotherhood
Latest government figures said at least 830 people have died since last Wednesday in clashes pitting followers of deposed Islamist president against security forces in the worst political bloodletting to rock Egypt in recent history.
Police have rounded up hundreds of Mr Morsi’s Brotherhood backers in recent days, in an effort by the army-backed government to end weeks of protests and to stamp their authority on the nation.
The latest deaths came as Egypt’s military leader vowed the army would not allow further violence, while still calling for the political inclusion of supporters of the country’s former president.
Defence minister General Abdel-Fatah el-Sissi, who led the 3 July coup that toppled Mr Morsi, again last night said the army has no intention of seizing power in the Arab world’s most populous country.
Gen el-Sissi’s comments came during his first appearance since a deadly attack on Wednesday on two encampments of Morsi supporters that left hundreds dead.
“We will not stand by silently watching the destruction of the country and the people or the torching of the nation and terrorising the citizens,” he said in comments quoted on state television and posted on an official military Facebook page.
The general said that the military did not seek power but instead “have the honour to protect the people’s will – which is much dearer [than] ruling Egypt”.
Gen el-Sissi called for Islamists to be included in the country’s politics. A military timetable calls for the nation’s constitution to be amended and for presidential and parliamentary elections to be held in 2014.
“We have given many chances … to end the crisis peacefully and call for the followers of the former regime to participate in rebuilding the democratic track and integrate in the political process and the future map instead of confrontations and destroying the Egyptian state,” he said.
The Muslim Brotherhood, under pressure since police stormed its protest camps in Cairo, said it was planning more marches to demand the reinstatement of Mr Morsi.
Coptic Christian minority suffers in days of rage as churches are looted and burned
After torching a Franciscan school, Islamists paraded three nuns on the streets like “prisoners of war” before a Muslim woman offered them refuge, a nun has said.
In the days since security forces cleared two sit-in camps by supporters of Egypt’s deposed president, Islamists have attacked dozens of Coptic churches along with homes and businesses owned by the Christian minority.
Christians have long suffered from discrimination and violence in Muslim-majority Egypt, where they make up 10 per cent of the population of 90 million.
Nearly 40 churches have been looted and torched, while 23 others have been attacked and heavily damaged since last Wednesday.
Sister Manal is the principal of the Franciscan school in Bani Suef. She was having breakfast with two visiting nuns when news broke of the clearance of the two sit-in camps.
In an ordeal that lasted about six hours, she, sisters Abeer and Demiana and a handful of school employees saw a mob break into the school, loot its contents, knock off the cross on the street gate and replace it with a black banner resembling the flag of al-Qaeda.
By the time the Islamists ordered them out, fire was raging at every corner of the 115-year-old building. Money saved for a new school was gone, said Sr Manal, and every computer, projector, desk and chair was hauled away. Calls to the police, including officers with children at the school, produced promises of quick response but no one came.
“They paraded us like prisoners of war and hurled abuse at us as they led us from one alley to another without telling us where they were taking us,” said Sr Manal.
At Minya, a Catholic school was burnt to the ground and a Christian orphanage was also torched.