Under a clause in Iceland’s penal code that traces its roots to 1940, offenders can apply for a process to have their “honor restored” — which gives them a right to seek a law license and removes a bar on them serving in other positions of responsibility — if three respectable citizens vouch for their character in letters of recommendation. The clause has come under criticism by advocates for victims of sexual abuse, and the Icelandic news media has pushed the Justice Ministry to release the names of those who have sought to make use of it.

Mr. Sveinsson’s letter, written in June last year, became public last week, but the justice minister, Sigridur Andersen, said that she had told Mr. Benediktsson about it two months ago.

Bright Future has accused the government of a “serious breach of trust” for concealing the existence of the letter, and politicians across the political spectrum have seized on the scandal to call for greater transparency.

Smari McCarthy, a member of Parliament for the anti-establishment Pirate Party, described the scandal on Twitter as “Iceland’s Jimmy Savile case,” referring to a British television personality who was revealed after his death in 2011 to have sexually abused dozens of adults and children.

Mr. Benediktsson said he had been shocked to learn of his father’s letter. “I want to stress that it was a shock for me to hear this,” he said at a news conference on Friday. “I could never have signed such a letter and I would never have defended such actions.”