Kemi Badenoch, the business secretary, is seeking urgent talks with Fujitsu to thrash out a compensation package for sub-postmasters affected by the Post Office Horizon scandal.

Sky News has learnt that Ms Badenoch wrote to Takahito Tokita, the Japanese company’s chief executive, in the wake of an acknowledgement from Fujitsu bosses that it had a “moral obligation” to contribute to the compensation bill.

In the letter, parts of which have been seen by Sky News, the minister wrote that she would “value the opportunity to discuss Fujitsu’s involvement in the Post Office Horizon scandal“.

“As you may know, my department is at the forefront of our government’s efforts to right the wrongs of the past.

“I am committed to ensuring that postmasters affected get the justice they deserve.”

“This is why the UK government announced new legislation last week, to overturn wrongful convictions and a plan to ensure swifter access to compensation.”

The scale of the eventual bill remains unclear, although ministers have said that the government has set aside £1bn to fund payouts to convicted and other affected sub-postmasters.

Government insiders believe that Fujitsu will be put under pressure to fund a substantial sum running to hundreds of millions of pounds after both it and the Post Office – which is owned by the government – lied and obstructed justice for many years.

On Tuesday, Paul Patterson, Fujitsu’s European chief executive, told MPs the company was “truly sorry” for its conduct, which has drawn renewed scrutiny after ITV broadcast Mr Bates vs the Post Office, a drama about what has been labelled Britain’s biggest-ever miscarriage of justice.

Kevin Hollinrake, the minister in Ms Badenoch’s department responsible for postal affairs, has been praised by some of those involved in the scandal for having repeatedly raised it in parliament while he was on the backbenchers.

Mr Hollinrake was also responsible for introducing £600,000 payouts last autumn for those whose convictions had been overturned.

He said earlier this week that negotiations with the company would be focused on “maximising the contribution to the taxpayer”.

“It’s a very significant bill [which] may end up north of £1bn.

“We should expect people who contributed to this scandal to contribute financially.”

Nevertheless, both Alan Bates, the architect of the original efforts to expose the fraud against sub-postmasters, and Jo Hamilton, another of the victims highlighted in the ITV drama, have criticised the bureaucracy attached to the compensation process.

“I understand that we are awaiting the conclusions of the Williams inquiry, but ahead of that I would welcome a discussion with you on the type of response Fujitsu might make and the role you foresee Fujitsu playing towards securing justice for those affected,” Ms Badenoch added in her letter to Mr Tokita.

One source said that Ms Badenoch had been scheduled to meet Fujitsu officials during a visit to Japan last year, but that talks had not taken place owing to diary clashes.

The Horizon contract is said to have earned £2.5bn for Fujitsu despite protracted and widespread warnings that the system was flawed.

To compound its role in creating the accounting software at the heart of the crisis, Fujitsu staff also gave evidence as expert witnesses during private prosecutions brought by the Post Office.

The scandal has raised questions about the behaviour of both the Japanese company and the Post Office, as well as the latter’s government shareholder body responsible for its oversight.