The Roman Catholic archdiocese of Boston has offered $55m to settle lawsuits by the alleged victims of sexual abuse by priests.
Bishop O'Malley has pledged to crack down on sex abuse in the church
Last year more than 542 people filed civil lawsuits against the archdiocese, saying they had been abused by clergy over the past six decades.
News of a settlement offer comes a week after Archbishop Sean Patrick O'Malley was installed as head of the fourth-largest Roman Catholic diocese in the United States.
Jeffrey Newman, a lawyer representing more than 200 of the alleged victims, welcomed the offer but said it was far from a done deal.
"We think it's a very good start, but it's only a start," he said.
Bishop O'Malley's predecessor, Cardinal Law, resigned amid public outrage in December following allegations he had moved paedophile priests from one pulpit to another rather than confront accusations that they had sexually assaulted children.
The new archbishop gained national attention for cracking down on sex abuse in his previous assignments.
He said that the sums of money required to settle the abuse lawsuits were "staggering" but no amount could compensate for the damage caused by abuse.
The offer on the table now is by far the largest so far, both in terms of the number of victims involved and the amount of money.
It follows the temporary suspension of court action earlier this year by both sides in an effort to negotiate an agreement.
For the settlement to go into force, it has to be accepted by at least 95% of the claimants who each have 30 days to decide.
The BBC's Jane Standley, in New York, says it is believed at least 1,000 children could have been abused over a period of more than 60 years.
Last year, the church reached a $10m settlement dollar with 86 victims of John Geoghan, a Boston-area priest whose criminal conviction for sexual abuse caused the scandal to come to light, our correspondent adds.
This June, the archdiocese of Louisville, Kentucky, agreed to pay more than $25m to 243 people who said they were abused by priests.
According to court documents obtained by Reuters news agency, the archdiocese agreed to make concessions in the latest offer.
These included waiving provisions for a statute of limitation, which would have required for accused priests to be still alive for claims to be considered.