Attorneys general from 44 states and territories urged Facebook Inc. to disown plans to initiate a version of Instagram for children, citing behavioral and privacy concerns regarding social media’s effects on young people.

In a letter to Facebook Chief Executive Mark Zuckerberg on Monday, the officials stated that the research has painted a joyless picture of children’s social-media use, referencing links to mental-health issues and bullying.

The letter adds bipartisan weight to pressure that Facebook has faced over its plans for an under-13-years-old Instagram version since March, when Mr. Zuckerberg spoke about the concept in a congressional hearing. In April, Democratic lawmakers also sent Mr. Zuckerberg a letter criticizing the plan. 

Facebook now restricts children under the age of 13 from joining its apps and websites, but Mr. Zuckerberg has acknowledged that many children joined by lying about their age.