The United Nations feared that up to 90,000 civilians could be stuck in the city which is running short of both food and water.
Fallujah, which is about 30 miles west of Baghdad, was captured by ISIS in early 2014.
Bigadier General Yahya Rasool said the escape route, known as 'al-Salam (Peace) Junction in the south west of the city.
Rasool said: 'There were exit routes previously, but this is the first to be completely secured and it’s relatively safe.'
An estimated 4,000 people have fled the city since the new escape route has opened up.
The al-Salam Junction route was secured after troops dislodged insurgents from districts located on the western bank of the Euphrates river, opposite Fallujah’s city centre on the east bank, said Rasool. He did not give a number for the civilians who were able to flee so far using it.
More than 20,000 people have managed to flee the city and its surrounding area since the Iraqi army began the offensive on May 23, the United Nations said on June 8.
Some 24,000 people have fled the city since the beginning of the offensive on May 23.
However, ISIS murdered 18 members of two families who attempted to escape on Friday.
ISIS snipers have been targeting civilians as they try and cross the Euphrates in a bid for freedom.
Relatives said the initial group that tried to sneak out of IS-controlled areas on Friday included around 100 individuals, including a majority of women and children.
The group were all from the same two families - Albu Hatem and Albu Saleh - and had made a previous failed attempt to leave days earlier.
'When they got near the intersection, which is the meeting point with the Iraqi forces, two gunmen on motorbikes arrived and sprayed them with gunfire,' said Ahmed al-Ghneim, a relative.
Two of the survivors, relatives from the Albu Saleh family, are staying at his home in Amriyat al-Fallujah, south of Fallujah.
'Some of the residents jumped into the canal, some fled to a nearby house. When they entered it, it blew up on them because it was booby-trapped,' he said.
'Some survivors were forced to go back inside Fallujah. Daesh took 17 of the wounded to Fallujah .
Sami Abu Hatem, a relative who was already living in a camp in Amriyat al-Fallujah, confirmed that version of events.
'Three of my direct relatives, a man with two young children, were among those massacred,' he said.
Abu Hatem he said he knew of 18 members of the group being killed and added that more were feared missing after jumping in the nearby canal.
According to aid groups running displacements camps outside Fallujah, only small numbers of residents have managed to flee the city centre.
Most of the 24,000 people who have escaped ISIS rule since the start of the operation three weeks ago are from outlying rural areas.
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