Campaigners welcomed what they saw as a pledge by Lord Penrose, chairman of the public inquiry, to "name names" where appropriate in his quest for the truth about what led to thousands of people becoming infected during the 1970s and 1980s.
But there was disappointment yesterday that the inquiry, which could take several years, will not look at the issue of increased compensation for victims, including a large number of haemophiliacs.
Almost 4,700 patients were infected through contaminated blood transfusions across the UK; about 2,000 have died.
Persistent calls for a full investigation led to the Scottish Government agreeing to a public inquiry last year.
The first session of the inquiry, held in Edinburgh, opened with a minute's silence for those affected. Lord Penrose said patients and families "deserve our deepest sympathy".
He went on to set out how the inquiry will operate and described it as "a daunting task".
The team will go through a vast quantity of documents already in the public domain before considering which witnesses will give oral evidence.
The inquiry has the power to compel witnesses to give evidence, although Lord Penrose said he hoped most would do so willingly.
However, under legislation it cannot compel civil servants or ministers from the UK government to give evidence.
Lord Penrose also said it would not be possible to find individuals or institutions legally liable, either in a criminal or civil sense. But he added: "It is highly likely that it will be necessary to consider whether it will be appropriate to identify people who did or failed to do things that might have made a difference, and to comment on their actions or failures."
He indicated it was possible his report would include criticisms of "individuals, groups, agencies and institutions".
But Lord Penrose said the issue of compensation for victims was not part of his remit.
In February a two-year privately funded inquiry by Lord Archer of Sandwell, sitting in London, ended with calls for more compensation for victims of tainted blood products.
Dan Farthing, of the Haemophilia Society, said: "Obviously we think compensation is appropriate and urgently needed in a lot of cases.
"It is disappointing that this amount of work (in the Penrose inquiry] is going to be done and won't then lead to a recommendation on compensation. But we are fortunate to have the Archer report covering the whole of the UK which has made recommendations on compensation."
But Mr Farthing welcomed the suggestion that the inquiry would be able to identify those who may be at fault. "There's a strong feeling no-one has accepted responsibility," he said.
"Lord Penrose talked quite strongly about how he would be prepared to name names and I think that is what will be new about Penrose. Lord Archer was not, legally, in a position to talk about actions of individuals."
Bill Wright, of Dunkeld, Perthshire, who contracted hepatitis C from a blood product in 1986, was at the hearing and welcomed Lord Penrose's "encouraging" approach.
"People want different things," he said. "Some want to see heads roll. Others want an apology, others want the truth to come out, others are in financial difficulty."