Keir Starmer will act on the findings of an independent investigation into Tulip Siddiq’s conduct regardless of the outcome, a cabinet minister has said, as Kemi Badenoch called for her to be sacked.

Badenoch, the Conservative leader, accused the prime minister of appointing “his personal friend as anti-corruption minister and she is accused herself of corruption”, after the Bangladesh government raised serious concerns about Siddiq’s links to the regime of Sheikh Hasina, her aunt.

The science secretary, Peter Kyle, rejected claims that Siddiq should resign while the independent adviser on ministerial standards, Sir Laurie Magnus, investigates allegations about properties linked to Siddiq’s family and her aunt’s political movement in Bangladesh.

Siddiq, the economic secretary to the Treasury, who is responsible for policy on the City and tackling corruption, referred herself to Magnus last Monday, asking for an investigation to be launched, and said she had done nothing wrong.

On the same day, the prime minister said Siddiq had “acted entirely properly” and that he had “confidence with her”.

However, the Sunday Times published remarks from Bangladesh’s new leader, Muhammad Yunus, who said Siddiq should apologise after reports she had lived in London properties with links to her aunt, who was deposed as prime minister of Bangladesh last year and is at the centre of a corruption investigation.

Yunus also said that properties used by Siddiq should be investigated and handed back to his government if they were gained through “plain robbery”.

It prompted the Conservative leader to call for Siddiq to be sacked. She posted on social media: “It’s time for Keir Starmer to sack Tulip Siddiq,” adding that the PM had “appointed his personal friend as anti-corruption minister and she is accused herself of corruption”.

Speaking to Sky News’s Sunday Morning with Trevor Phillips, Kyle said: “I think she’s done exactly the right thing, she’s referred herself, that inquiry needs to go through.”

He added: “I think the right way to go through this is to allow the authorities to investigate. We have given more powers to those authorities to do independent investigations, and you know full well when it comes to Keir Starmer he will listen to what the authorities say.”

When challenged that Labour in opposition would have said the minister should be sacked while being investigated, Kyle contrasted this approach with an investigation under the previous government into Priti Patel for allegations of bullying while she was home secretary.

Kyle noted: “The results came out, she was found guilty, and no action happened.”

The shadow chancellor, Mel Stride, said Starmer should “get a grip” and sack Siddiq as it had become “impossible” for her to do her job due to the allegations.

Stride told the programme: “What is not right is that the prime minister is not moving her out of that position and getting her to step down.

“Because she is the anti-corruption minister, she has serious charges laid against her now, or serious accusations around corruption, and it’s going to be really impossible for her to do that job under current circumstances. So she should step down, and the prime minister needs to get a grip of that.”

He added: “There are circumstances, I think, where you are in a situation where you cannot actually do your job effectively. Now look, the chancellor has gone over to China; Tulip Siddiq, my understanding was that she was due to be joining her, now she hasn’t, and I would imagine, joining the dots, that’s because of the circumstances surrounding her at the moment.

“So at the moment, she’s not in a position to be able to properly carry out her role in government, and the prime minister needs to get a grip and to move her on.”

• Keir Starmer
• Kemi Badenoch
• Labour
• Conservatives
• Peter Kyle
• Bangladesh
• news