The government offered payments of $77,600, an amount unlikely to satisfy many of the families, The Belfast Telegraph reported Friday
Negotiations with families have been going on for months
One woman, Kate Nash, said "all the money in the world" won't bring back her brother, William, 19, who was among 13 protesters killed by paratroopers Jan. 30, 1972.
Alex Nash, the siblings' father, was among 13 people injured. He died in 1999.
Kate Nash said she "became slightly outraged" when the government offer was made.
"My father was in a bunker watching his son die," she said. "How in terms of compensation could you ever make up for that?"
"My father was not just physically seriously injured, he was mentally seriously injured."
The Saville Report, published in June 2010 after 12 years of investigation, found soldiers killed the protesters without justification.
Prime Minister David Cameron apologized to the families and called the killings "unjustified and unjustifiable."
Couple mistakenly served bag of cash at McDonald's drive-thru
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'