Witness Samira Lamrani said tower residents could be seen at their windows, panicking.
"People were starting to appear at the windows, frantically banging and screaming," she told The Telegraph.
"Us members of the public were reassuring them, telling them we've done what we can and that we've phoned 999, but obviously the look on their face was death."
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Lamrini then said she saw a woman from a ninth or tenth story window with a baby.
The woman signaled she was going to drop the child to those below, crying out "I'm about to throw my baby. Please catch the baby!" according to Lamrani.
Moments later, she did.
A man ran from the crowd of witnesses to catch the falling child. He then took the child to safety.
Lamrani calls it was a "miraculous" rescue.
A resident named Zara, also said she saw a child thrown from the fifth or sixth story.
She believes he also survived. "I think he might have just had some broken bones and bruises," she said.
At least 17 others were killed in the fire. Many others are still listed as missing and all 120 apartments in the tower were destroyed.
Rescue workers continue to search through the rubble as a structural engineer keeps watch as there is a danger of the tower collapsing.