Catriona Ogilvy, 34, has called on Rt Hon Savijd Javid MP at the department for Business, Innovation and Skills to recognise the needs of families with children born prematurely, with currently 8,200 signatures.
Ogilvy began the Change.org petition - The Smallest Things - three months ago.
It's a campaign close to her heart as her son Sam, now four, was born unexpectedly at 30 weeks.
Ogilvy said she was unaware maternity leave would begin the day after he was born, as she waited weeks before she could even hold her baby.
"The reality of life in neonatal care is very different from what a mother would usually expect from the early days of maternity leave," the mother wrote on her petition page.
"[My son] was transferred to the neonatal intensive care unit breathing on his own and I like to think that was him showing us his fighting spirit from the get-go.
"Shattered and numb we spent just a short while with our new baby; holding his hand through the portholes in his incubator, taking hazy pictures through the perspex box."
Ogilvy said she went home without her baby and felt "empty" and plagued with guilt.
She continued: "Your life becomes the neonatal unit and the emptiness is quickly filled with a three-hourly expressing routine, endless trips to and from the hospital and hours spent waiting; waiting for that precious moment when you can hold your baby for the first time.
"The moment comes and your overwhelming instinct is to hold them close, to kiss and cuddle them, but wires and tubes are in the way and you hold them at a distance wondering when you’ll next get this chance.
"Then it’s back into their box and the watching and waiting starts over again."
Writing about the reason for extended leave, Ogilvy added: "Extending statutory maternity leave and pay would give mothers the emotional and financial support needed at a time of great stress and trauma - in turn leading to better postnatal health, a more positive return to work and better outcomes for babies development."
Ogilvy has since had a second son, now two, who she said was also born prematurely.
Ogilvy with her son Sam on the day she brought him home from hospital
Commenting on the petition, a mother whose daughter was also born 10 weeks premature said she wasn't emotionally ready to return to work.
She wrote: "My maternity pay at full rate ended while my daughter was still in the NICU.
"As the highest-waged parent I was forced to return to work sooner than I would have liked. Our daughter was still ill, this led to an eight-month bout of postnatal depression for me and bonding issues with my daughter.
"I would have given anything to have spent more time at home with Martha getting her well, and getting to know her - I spent the first few months not letting myself get overly attached in case we lost her. We barely got her home when I had to return to work - emotionally I wasn't ready."
Another mother described her maternity leave as being "the most distressing experience".
She wrote: "My daughter was born 16 weeks premature and was in hospital for six months, then on oxygen for a further six months at home.
"The most distressing experience and to have to think about going back to work before she was even off oxygen would add to the stress. Please try to imagine the agony of parents in this heartbreaking situation."
To sign the petition, please click here.