Lively then said she appreciated the news outlets who avoided using pictures of celebrities' children.
"Thanks to everyone else for all the love and respect and for continuing to unfollow accounts and publications who share photos of children.
"You have all the power against them. And thank you to the media who have a 'No Kids Policy.' You all make all the difference."
The photos on Lively's Instagram show her with her husband and other family and friends, including pop star Taylor Swift.
Lively and Reynolds already have three daughters – James, 7, Inez, 5, and Betty, 2.
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