The Brisbane mother on the run with her children in Lebanon.

A mother and her two children are on the run after an alleged child recovery operation went awry in Lebanon.

The operation which also saw Sixty Minutes‘ Tara Brown and a film crew detained by Lebanese police, is ongoing with no confirmed reports as to the current location of the mother and her two young children.

Sally Faulkner reportedly travelled to Beirut to recover her children, Lahela, 5, and Noah, 2, from their father Ali Elamine.

Faulkner was reunited with her children after they were snatched at a bus stop by men in a silver Hyundai while waiting for a bus with their paternal grandmother, according to smh.com.au.

Lebanese media reported the incident involved guns and injury to the children's grandmother.

Until the recent interception, it had been almost a year since the Brisbane mother had seen her children.

The last time she saw them was in May 2015, on the day they were allegedly taken to the airport by Elamine for a holiday.

Since then, Faulkner has launched several online campaigns to raise awareness for her situation in hopes it will garner federal attention.

In a heartbreaking video addressed to Foreign Minister Julie Bishop, Faulkner begs the minister for intervention.

“My children were born in Australia and have lived with me all of my life." Faulkner said.

“I need you to do something to help bring my babies home.”

A change.org petition was also set up that has amassed over 33,000 signatures in support.

"My little Lahela and Noah were taken seven months ago. They were terrifyingly put on a plane by my ex-husband and I haven't heard from them since." Faulkner wrote.

"This man stole my kids quietly and will face no punishment. I'm worried every second of the day if they are okay and safe."

Faulkner has claimed that Elamine told her the children would never return to Australia, The Daily Mail reports.

Fairfax Media reported a border alert has been sent out which will likely stop them from escaping the country.

Lebanese media have also reported that Elamine claimed Faulkner was comfortable with him taking the children and only began to protest when he stopped making maintenance payments.

Experts have estimated the recovery operation could have cost upwards of $80,000.

It is being claimed by Lebanese media this CCTV footage captures the moment the children were taken from their grandmother.