Nearly 1,200 UK television freelancers and executives signed the letter accusing the Good Morning Britain presenter of bullying former colleague Adeel Amini on social media.
ITV has said in a statement: "ITV takes any allegations of bullying and harassment in the workplace very seriously indeed, and we are clear there is absolutely no place for it in ITV.
"We have an independent whistleblowing helpline which we communicate through our induction process and which we monitor on an on-going basis, in addition to our internal grievance procedures channels, which are open to both permanent members of staff and freelancers.
"Our firm understanding is that in this instance, the tweet in question was not accusing Piers of bullying and harassment whilst working on Life Stories. Having spoken to both parties, there is therefore no internal investigation.
"In terms of the separate issue of social media exchanges, we understand some producers wish to express their views on their personal platforms, and we also think it is widely understood that Piers is a prolific and long-standing user of social media where he is well known for engaging in robust, heated exchanges, when criticism is levelled against him.
"However, Twitter accounts and the decision to comment on each other are their personal choices.
"Piers is a freelance presenter and we do not control his output on social media, or the other media platforms he writes for."
The broadcaster added: "To reiterate, we are clear there is no room for bullying at ITV and it is not tolerated. We are supportive and engaged members of Coalition for Change, and we will continue to work productively with colleagues across the industry."
The claims of bullying came after Morgan, 55, hit out at researcher turned producer on Twitter after he said he regretted working on Piers Morgan's Life Stories early in his career.
Morgan hit back: "Hi Adeel, you spent precisely two months working on Life Stories in 2010 & judging by your CV that was the pinnacle of your TV career. So you really don’t need to worry about getting any more job offers from me because I’d rather employ a lobotomised Aardvark."
Referring to the accusations on social media Morgan also referred to Amini as an "abusive hypocrite".
Amini worked as a researcher on Life Stories back in 2010.
Responding to ITV's statement he said: "While I agree that it is not down to ITV to police the social media of freelancers, there comes a line when moral responsibility ought to shine over business viability. It is not good enough to 'Get Britain Talking' and turn away from the root causes of poor mental health."
The open letter to ITV CEO Carolyn McCall and Kevin Lygo, managing director of media and entertainment, expressed concern that Morgan is “directing targeted abuse” towards a freelancer.
They wrote: “As freelancers working within television, we feel a responsibility to speak out against bullying and harassment wherever we see it, including from on screen personalities who are all too often poorly reprimanded for unacceptable behaviour and abusive conduct.”
Watch: GMB guest asks Piers Morgan 'Who are you?'