Buckingham Palace said it was "very concerned" about reports in the Times newspaper on Wednesday that assistants working for Meghan, the Duchess of Sussex, had been bullied by her.
The report comes days before the broadcast of an interview that Meghan and her husband Prince Harry have given to US chat show host Oprah Winfrey spelling out why they quit their official roles. Some commentators have suggested they may also criticise their treatment by the royal family.
Harry and Meghan issued a statement denying that she had bullied anyone.
The Times cited unnamed sources as saying an aide to the couple had raised a complaint in October 2018 alleging that Meghan had reduced some of her assistants to tears and treated others so badly that they had quit.
The paper said Harry had urged the aide, who has now left their staff, to drop the complaint, and it never progressed.
The Times said it had been contacted by former staff members who wanted the public to gain insight before the Winfrey interview aired - and that lawyers for the couple had labelled the allegations a smear orchestrated by the Palace.
Reuters could not independently verify the report.
"We are clearly very concerned about allegations in The Times following claims made by former staff of The Duke and Duchess of Sussex," Buckingham Palace said in a statement.
The Royal Household "does not and will not tolerate bullying or harassment in the workplace", it added.
It said its HR team would look into the allegations, and that members of staff involved at the time would be invited to participate.
"SADDENED BY ATTACK"
There was no immediate response from Harry and Meghan to the Palace statement.
A spokeswoman had earlier said Meghan was "saddened by this latest attack on her character, particularly as someone who has been the target of bullying herself and is deeply committed to supporting those who have experienced pain and trauma".
It added: "She is determined to continue her work building compassion around the world and will keep striving to set an example for doing what is right and doing what is good."
Meghan and Harry, who married in May 2018, stepped back from their official duties in March last year to forge new careers and a financially independent life in California.
That decision was confirmed last month, when they also handed over all their royal patronages. They said their move was fuelled in part by intense press intrusion.
However, Meghan had also previously indicated that she felt she did not have the full support of the royal family.
In court documents submitted as part of her successful privacy action against the mass-circulation Mail on Sunday, her lawyers said she had felt "unprotected" while she was pregnant with their son Archie.
Royal biographer Penny Junor told Reuters the Winfrey interview was likely to be frank.
"I suspect there will be snipes at the royal family. There will probably be a justification for their leaving, which the royal family will probably find uncomfortable," she said.
"My biggest fear, I suppose, is that Meghan and Harry say things about their family that they will regret."