Jess Phillips says she would not have resigned if Sir Keir Starmer had announced an under-16s social media ban earlier.
The prime minister announced on Monday that the new restrictions would come into force early next year to protect the "happiness of our children".
Speaking on the Electoral Dysfunction podcast, Ms Phillips said the move would have kept her in government.
"This would've been enough to keep me in the tent," Ms Phillips said.
"Not only would it have been enough to keep me in the tent. I told them that. I was explicit about that.
"I spoke to various different people in Number 10 and really tried to push them to say, look, look, go for this. This is a bold move. This is bold and it is big and it is brave and it's the right thing to do."
You can listen to the full conversation on the Sky News Insider edition of Electoral Dysfunction.
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Ms Phillips stepped down as safeguarding minister last month following Labour's dismal local election results, accusing Sir Keir of lacking the "drive to get anything done".
She also said restrictions on social media use should not "stop at kids".
"I don't think the algorithm should exist. Full stop," she said.
From next spring, under-16s will be banned from using all the main social media sites, including Instagram, Snapchat, YouTube, Facebook, and X - although messaging apps like WhatsApp won't be banned, and neither will educational sites like YouTube Kids.
Ministers are also looking at an overnight social media curfew for 16 and 17-year-olds, as well as banning infinite scrolling.
Starmer wants a 'legacy'
Ms Phillips also said Sir Keir had announced a ban "almost certainly" because he wanted to leave a "legacy".
She continued: "Men love [a] legacy, don't they?
"I cant give a toss about how I'm remembered, but here we are. But like, it was definitely the language we used to use to try and get things over the line. Like, this would be an amazing legacy."
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