The apologies followed publication of Sir Brian Langstaff's final report as part of the Infected Blood Inquiry which documented a ‘subtle, pervasive and chilling' cover-up to conceal evidence.
Around 30,000 people were infected with hepatitis and HIV while receiving NHS treatment between the 1970s and 1990s, with 3,000 having since died.
The Prime Minister said publication of the report marked a 'day of shame for the British state' and highlighted 'decades-long moral failure at the heart of our national life'.
'I want to make a wholehearted and unequivocal apology for this terrible injustice,' Sunak said.
Government minister John Glen said interim payments of £210,000 would be paid within 90 days to victims.
Amanda Pritchard, chief executive of NHS England, said tens of thousands of people had been 'badly let down' and offered her 'deepest and heartfelt apologies for the role the NHS played in the suffering and the loss of all those infected and affected'.
Pritchard said a bespoke psychological support service for those affected will be ready to support its first patients later in the summer and offered reassurances that 'rigorous modern safety standards continue to ensure that the NHS blood supply is now among the safest in the world'.