The dean of the college of cardinals, Cardinal Angelo Sodano, will celebrate Law's funeral Mass today behind the main altar of St. Peter's Basilica.
Following the typical protocol, Francis is expected to preside over a final prayer, a blessing with incense and the sprinkling of holy water around Law's coffin.
US Ambassador-designate Callista Gingrich and her husband, Newt, as well as some other members of the diplomatic corps were on hand in the pews, along with the Vatican foreign minister, Archbishop Paul Gallagher.
One of the opening prayers reads: "O God, who chose your servant Cardinal Bernard Law from among your priests and endowed him with pontifical dignity in the apostolic priesthood, grant, we pray, that he may also be admitted to their company forever."
More From This Section
Law, who died yesterday at age 86, resigned in disgrace as archbishop of Boston in 2002 after revelations that he covered up for dozens of priests who raped and sexually molested children, moving them to different parishes without telling parents or police.
St John Paul II's decision to promote Law to head a major Rome basilica in 2004 reinforced the impression that the Vatican -- which had turned a blind eye to abuse for decades -- still hadn't grasped the scale of the problem, the trauma it caused its victims, and the moral credibility it had lost as a result.
Just this week, Francis' much-hyped commission of experts to advise the church on keeping children safe was allowed to lapse after its initial three-year mandate.
Sodano was John Paul's powerful secretary of state at the time of Law's downfall and would have been instrumental in the decisions the Vatican took in those years to deal with the burgeoning scandal.
Sodano, who presides over all funerals for Rome-based cardinals, often offers a eulogy, though it is not transcribed or published by the Vatican.