The summit was announced a day before Francis will meet American church leaders hit by fresh accusations over the cover-up of sex abuse by priests.
Vatican spokesperson Greg Burke said DiNardo and O'Malley would meet with Francis on Thursday in the Apostolic Palace.
The council also expressed their "full solidarity" with the Pope after Archbishop Carlo Maria Viganò released an 11-page dossier calling on Francis to resign and accusing him of being informed about McCarrick's behaviour.
In an 11-page statement published on August 26, Archbishop Carlo Maria Vigano, the former Vatican ambassador to Washington, launched an unprecedented broadside by a church insider against the Pope and a long list of Vatican and US church officials.
Allegations that Pope Francis lifted restrictions from now ex-Cardinal Theodore McCarrick despite knowing he was a sexual predator are "grave charges" that "must be investigated and shown either true or false", said Indiana Bishop Donald Hying.
Many have called for Wuerl's resignation, including Catholic teachers who have protested outside his services, amid allegations he tried to hide claims child sex abuse.
On Tuesday, he drew Satan into the fray, suggesting that the devil was behind Vigano's revelations.
"In these times, it seems like the Great Accuser has been unchained and is attacking bishops", the pontiff said. "He tries to uncover the sins, so they are visible in order to scandalize the people".
Bishops, he said, should be men of prayer, and should know they were chosen by God and keep close to their flock.
In the USA, a grand jury report released last month from Pennsylvania found that more than 300 priests had sexually abused minors in the state over seven decades.
The three who were absent were: 85-year-old Cardinal Francisco Javier Errazuriz Ossa, retired archbishop of Santiago, Chile, who is facing questioning over his handling of abuse allegations; Cardinal Laurent Monsengwo Pasinya of Kinshasa, Congo, who turns 79 in early October; and 77-year-old Australian Cardinal George Pell, who now is on trial in Australia on sex abuse charges.
Archbishop Georg Gaenswein, a top aide to both retired Pope Benedict XVI and Pope Francis, told a book presentation Tuesday that he by no means was comparing the scandal to the almost 3,000 people killed in the US on September 11, 2001.
In Cardinal Wuerl's letter to the priests, which was obtained by LifeSiteNews and confirmed by the Archdiocese of Washington that it was sent on Tuesday, he discusses a resignation letter that he submitted in November 2015.