Badenoch has written to Fujitsu Chief Executive Takahito Tokita, in a letter which was reported by Sky News as saying she would "value the opportunity to discuss Fujitsu's involvement in the Post Office Horizon scandal."
A Fujitsu spokesperson in Japan could not be reached for comment outside normal business hours, while Britain's business and trade department declined to comment.
The over 20-year scandal saw hundreds of sub-postmasters wrongfully prosecuted or convicted of false accounting, theft and fraud after the Fujitsu-developed Horizon software incorrectly showed money missing from the accounts of Post Office branches.
The British government last week announced plans to introduce new legislation to overturn the wrongful convictions.
Fujitsu's European boss said on Tuesday he thought there was a "moral obligation" for the Japanese IT group to compensate victims of the scandal.
A recent TV dramatisation of the scandal - one of the biggest miscarriages of British justice - has caused renewed public outrage and demands for speedier justice for the victims.
"As you may know, my department is at the forefront of our government's efforts to right the wrongs of the past," Badenoch was quoted by Sky as saying in her letter.
"I am committed to ensuring that postmasters affected get the justice they deserve."
(Reporting by Juby Babu and Sachin Ravikumar; additional reporting by Satoshi Sugiyama, editing by Sarah Young)
