But the son of one of the victims said that the apology does not “feel genuine”.
The government told the inquiry on Wednesday the treatment of information surrounding the use of contaminated blood products has been “at worst, a cover-up, at best a lack of candour about past events”.
Eleanor Gray QC made the comments to the Infected Blood Inquiry on behalf of the Department of Health and Social Care.
The public probe will consider the treatment of thousands of people in the 1970s and 80s who were given blood products infected with HIV and hepatitis viruses.
The inquiry has pledged it will consider “whether there have been attempts to conceal details of what happened” through the destruction of documents or withholding of information.
Ms Gray told the inquiry: “I say unreservedly that we are sorry. We are sorry that this should be so, that this should have happened when it should not.”
She said “things went wrong,” and that the Department of Health “welcomes this inquiry and are committed to co-operating with it and assisting it”.
Jason Evans, 29, said he was not convinced by the apology.
His father Jonathan was born with haemophilia, but died in 1993 aged 31 having contracted hepatitis and HIV from the transfusion of Factor VIII blood products. Jason was aged just four.
He said: “What the Department of Health say and what they’re doing are two different things.
“My main takeaway from the Department of Health’s statement was that the QC admitted what happened was wrong.
“They admit wrongdoing, but continue to fight myself and about 700 others on the same issue in a group legal action at the High Court.
“It just doesn’t feel genuine to me.”
The inquiry has heard from a number of victims of the scandal over the last three days.
On Wednesday, Peter Burney accused the government of a “cover-up on an industrial scale,” which “reads like something out of a spy novel”.
He contracted hepatitis after two blood transfusions in 1976.
Offering his condolences to the families of those who died, Mr Burney said: “To watch someone you love pass through no fault of their own – the responsibility of others – takes the Great out of Great Britain.”
Michelle Tolley, 53, contracted Hepatitis C from blood transfused in 1987 and 1991 after childbirth.
She said of her infection on Tuesday: “The impact has been one of devastation, destruction and ultimately death.
“Those responsible for this tragedy must be identified, must be held responsible for their actions, and prosecuted if necessary.”
Chairman of the inquiry, retired judge Sir Brian Langstaff said on Monday it is estimated that the number of infected could reach above 25,000.
The inquiry will continue next year.