Dominic Raab has requested an investigation into himself following two formal complaints made against him after days of bullying allegations.

The deputy prime minister and justice secretary has written a letter to Rishi Sunak asking for an independent investigation into the complaints, one regarding his time as foreign secretary and another while he was justice secretary under Boris Johnson.

“I look forward to addressing these complaints, and continuing to serve as deputy prime minister, justice secretary, and Lord Chancellor,” he tweeted.

Mr Sunak has agreed an investigation should take place.

Raab to face Rayner at PMS – live politics updates

Mr Raab will face MPs at midday as he is taking Prime Minister’s Questions on behalf of Mr Sunak, who is in Bali for the G20 summit.

Over the past week, Mr Raab has faced bullying allegations in the media, including throwing tomatoes at staff, being rude to staff and being warned about his behaviour.

He has denied all the claims.

In his letter to Mr Sunak, the deputy PM said he had “just been notified that two separate complaints have formally been made against me”.

He did not say what the complaints were about and who had made them.

But he requested an investigation into the complaints “as soon as possible” and said he will “cooperate fully and respect whatever outcome you decide”.

He added: “I have always sought to set high standards, and forge teams that can deliver for the British people amidst the acute challenges that we have faced in recent years.

“I have never tolerated bullying, and always sought to reinforce and empower the teams of civil servants working in my respective departments.”

Read more: The allegations against Dominic Raab

Mr Sunak replied to his deputy’s letter and said he agreed to address the complaints against him.

“Integrity, professionalism and accountability are core values of this government. It is right that these matters are investigated fully,” he said.

It is not known who will head up the investigation into Mr Raab as there is currently no ethics adviser after Lord Geidt quit in June.

Mr Sunak’s official spokesman said yesterday the PM is “committed” to installing a replacement and the “process is ongoing to appoint a new adviser”.

The chair of the FDA civil servants union, Dave Penman, told Sky News on Tuesday there were allegations against several other current ministers but staff are not making official complaints as the system does not support them.

Labour’s Lisa Nandy, who was shadow foreign secretary while Mr Raab was foreign secretary, told Sky News it was an “open secret” bullying was going on in his office. Mr Raab’s spokesman denied the allegations.