In the original interview the duke and duchess of Sussex made a series of allegations against the royal family.
Meghan told the US television icon that there were "concerns and several conversations" with Prince Harry about "how dark Archie's skin might be when he was born".
The bi-racial actress declined to say who it was that had the conversations with her husband about Archie's skin colour as it would be "very damaging" to them.
She added that she suffered with her mental health during her time as a senior royal, stating she "didn't want to be alive anymore" and claimed she sought help from a senior member of the royal family but never received it.
Charles Anson, who worked as the Queen's press secretary from 1990 to 1997, told the BBC he believed there's not "a strand of racism within the royal household at all" but added the couple's comments "need to be considered".
In response to Meghan's comments about her mental health, Anson said that there is a "medical household" within the palace structure which he remembered being "very responsive" to members of staff and members of the royal family.
The opposition Labour party meanwhile is calling for an investigation into Meghan's claims.
Shadow Education Secretary Kate Green said the allegations of racism were "distressing, shocking" and urged Buckingham Palace to treat them "with the utmost seriousness" and said they should be "fully investigated".
In Oprah's follow-up with CBS This Morning on Monday, she revealed Prince Harry had told her it was not his grandmother nor his grandfather that were part of those conversations about Archie's skin colour.
Winfrey said Harry had not told her which member of the royal family was involved in the conversation.
"He did not share the identity with me but he wanted to make sure I knew, and if I had an opportunity to share it, that it was not his grandmother or grandfather that were part of those conversations.
"He did not tell me who was a part of those conversations."
In other new clips released on Monday, Harry said a large part of the reason he and Meghan left England for a life in the US was due to the racism in the UK.
In the new footage, when Winfrey asked if the couple left because of racism, the prince replied: "It was a large part of it."
He added he was urged by an unnamed person at a fundraiser for his charity Sentebale to not "do this" with the media as "they will destroy your life".
Harry said he was told: "You need to understand that the UK is very bigoted," to which he replied: "The UK is not bigoted, the UK press is bigoted, specifically the tabloids."Harry added: "But unfortunately if the source of info is inherently corrupt or racist or biased then that filters out to the rest of society."
Harry also claimed no one from the royal family has apologised to him and Meghan when they revealed they needed to leave the family due to a lack of support they felt they were having.
Buckingham Palace has yet to release a statement or comment on the interview.
A spokesperson for Prime Minister Boris Johnson has declined to comment on Meghan's allegations of racism towards her son, Archie, by a member of the royal household, adding that Johnson has not watched the interview.