Cardinal Luis Antonio Tagle of Manila also issued a statement urging people not to be distracted by Duterte's statement questioning God and God's ways.
"To those who blaspheme God as stupid, St. Paul's words are to the point".
The one-one-meeting between Duterte and Valles had been preceded by the President's tirades against God Himself, whom he called "stupid".
Duterte's latest remarks about God came July 6 at the opening of a science and technology event in Davao City, Philippines, where he noted he does believe in a supreme being, but not the biblical God.
"You do that (take selfie) today, one single witness that there is a guy, a human being, who's able to talk and to see God". He would say, 'Mayor, someone from the church ordered me to go to heaven and speak to God. "And if there is one, ladies and gentlemen, I will announce my resignation immediately", he said.More news: Rosberg Vehemently States Ferrari Crash to be Unintentional
Amid the criticisms, officials have arranged a meeting between Duterte and the head of the largest association of Catholic bishops on Monday.
In several pronouncements, Duterte claimed that he was a victim of abuse by a priest during his childhood.
"'For the stupidity of God is wiser than human wisdom, and the weakness of God is stronger than human strength, '" Valles said in the document read on national television by Caloocan Bishop Pablo Virgilio David, CBCP vice president.
"President Duterte agreed to a moratorium on statements about the Church after the meeting", presidential spokesman Harry Roque told newsmen.
"Duterte is distancing himself from many Catholics - the people who voted him to office", he said.More news: Donald Trump defends US position against global breastfeeding resolution
"So when you criticise me, do not use the platform of God, that God will send you to hell, that God will never forgive you, hell is waiting for you". This argument will die down by itself.
The firebrand president is due to hold talks at Catholic Bishops' Conference and also with Davao Archbishop Romulo Valles on Monday at Malacanang. Besides, I don't need to defend God in all of this. Do not take God - God's name in vain.
According to data reported by the Philippines' Phil Star news website, the nation's approximately 100 million residents include 87 million Christians, with 76 million identifying as Catholic and 11 million identifying as Protestants and "other Christians".
Duterte and Valles are natives of Davao with the latter serving as its archbishop prior to his election as CBCP president in July 2017.More news: Air India follows Japanese airlines in changing status of Taiwan