Andrew, the younger brother of King Charles, said last week he would no longer use his Duke of York title among others, following years of criticism about his behaviour and connections to the late US sex offender Jeffrey Epstein.
"We agree and support the decision that the royal family and Prince Andrew have taken," Bridget Phillipson, education minister and senior member of parliament, told Sky News.
"We believe that's the right course of action."
When asked about calls for the removal of Andrew's Prince title, Phillipson said it was not a matter for the government but one for the royal family to decide.
Prince Andrew and the royal family took the action ahead of the publication of Epstein victim Virginia Giuffre's memoir.
Meanwhile, Britain's Metropolitan Police said they would look into claims in the Mail on Sunday that Andrew had passed Giuffre's date of birth and social security number to his taxpayer-funded bodyguard in 2011 and asked him to investigate.
He is also said to have emailed the Queen's then-deputy press secretary and told him of his request to his protection officer, and also suggested Giuffre had a criminal record.
"We are aware of media reporting and are actively looking into the claims made," a Met spokeswoman said.
The allegations are the latest to emerge against the prince, who relinquished his dukedom and other honours on Friday, after excerpts from the posthumous autobiography of Giuffre were released.
The book is to be published on Tuesday, a day before Charles begins a state visit to the Holy See, during which he will become the first British monarch to pray at a public service with the Pope since the Reformation.
Charles, Supreme Governor of the Church of England, and Pope Leo will pray together during an ecumenical service in the Sistine Chapel, a symbolic moment of the continuing dialogue between their two churches.
The two-day visit to the Holy See is understood to be deeply significant for the King personally and will celebrate the papal jubilee held every 25 years.
A report in The Sunday Times suggested that the Prince of Wales was "not satisfied" with the decision concerning Andrew's titles.
The newspaper suggested William intended to take a "more ruthless" approach to his disgraced uncle, and would ban him from his future coronation.
It is understood, however, that the King and William are in lockstep over how to deal with the former duke.
Giuffre's brother, Sky Roberts, has urged the King to go further and strip Andrew of his right to be a prince.
Charles is said to have acted, in consultation with William, Andrew and the royal family, after it emerged Andrew had emailed Jeffrey Epstein in 2011 saying "we're in this together", three months after he claimed he had broken all contact with him.
In 2022, the then-Duke of York paid millions to accuser Giuffre to settle a civil sexual assault case, despite claiming never to have met her.
The prince's 2019 Newsnight interview, which he hoped would clear his name, backfired when he said he "did not regret" his friendship with convicted paedophile Epstein, who trafficked Giuffre.
He was heavily criticised for failing to show sympathy with the sex offender's victims.
Giuffre alleged, which Andrew vehemently denies, that she was forced to have sex with the prince on three occasions, including when she was 17, after being trafficked by Epstein.
With Reuters
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