In an open letter, Cardinals Burke and Brandmüller say the Church has wrongly blamed the abuse of power by clergy as the main cause of the scandals.
Instead, they say the cases involve priests who have “gone away from the truth of the Gospel”.
They also openly criticise the Pope.
Stories of sexual abuse of minors have emerged across the world and the Church has been accused of covering up crimes committed by priests.
Cardinals Raymond Burke, from the US, and Walter Brandmüller, from Germany, reject that the cases of abuse are a result of “clericalism” – a group of men abusing their power, and protecting each other.
The cardinals belong to the traditionalist wing of the Church, where many believe homosexuality is a root cause of the clerical abuse, and are both outspoken critics of Pope Francis.
“The plague of the homosexual agenda has been spread within the Church, promoted by organized networks and protected by a climate of complicity and a conspiracy of silence,” they said.
“Sexual abuse is blamed on clericalism. But the first and primary fault of the clergy does not rest in the abuse of power but in having gone away from the truth of the Gospel.”
In the Catholic hierarchy, cardinals are second in importance only to the pontiff, and there are currently 223 of them.
Cardinal Burke has links to former Trump White House adviser Steve Bannon, who will reportedly be in Rome during the summit.