In her statement posted on Wednesday evening, Ms Sturgeon said: “I don’t have much time for anything other than the fight against Covid right now but on some days silence is not an option.”
It follows reports of “significant numbers” of young people leaving the party over trans rights during the day.
Ms Sturgeon said: “Over the course of the day I've heard reports of young people in significant numbers leaving the SNP.
"I know many of you personally - I consider you friends, I have campaigned alongside you. You are a credit to our party and our country. It grieves me deeply that you've reached this conclusion after much soul searching because you consider at this stage the SNP not to be a safe, tolerant or welcoming place for trans people
"That is not acceptable to me - as SNP leader I will do everything I can to change that impression and persuade all of you that the SNP is your party and you should come home where you belong.”
The message also comes after Teddy Hope, who held a high-profile position as a trans officer in the Out For Indy wing of the party, resigned last week, claiming that the SNP party was ‘a hub for transphobia in Scotland.’
The First Minister admitted that within the party there were differences surrounding gender recognition reform however said this should be ‘debated respectfully’ and not used as a ‘cover’ for transphobia.
She added: “Trans people have as much right as any of us to be safe secure and valued for who they are.”
"Transphobia is wrong and we must treat it with a zero tolerance as treat racism and homophobia.”
She said that the message was ‘not planned’ or ‘scripted’ but came ‘from my heart.’
The SNP leader said that some may say the message did not go far enough or ‘too woke’ however Ms Sturgeon said she did not care as “sometimes particularly as a leader it is vital to speak up for what is right and against injustice.”