"This lack of support came at the moment I found myself in the most difficulty," he said in a letter published Wednesday in Italian daily Il Giornale, a newspaper owned by Berlusconi's brother Paolo.
Following heavy rains late last yer, Pompeii was hit by three cave-ins in less than a month.
The collapse in November of part of its frescoed House of the Gladiator and a wall at the site of the House of the Moralist prompted headlines around the world.
The collapses were followed by another cave-in at an ancient house in Pompeii in early December. The opposition blamed Bondi and said neglect and a cut in funding for the fragile archaeological site had caused the tragedy.
He survived a January no-confidence vote in Parliament tabled by Italy's centre-left opposition.
The opposition blamed Bondi for the Pompeii collapses and said neglect and a cut in funding for the fragile archaeological site had caused the tragedy.
The minister denied the accusations, saying his government had done its best to preserve and restore Italy's artistic heritage, and rejected calls for his resignation.
The culture mnistry press office told Adnkronos International by phone that no date had been set for Bondi's resignation.
"Berlusconi...knows about my decision to leave the ministry and will deal with the issue as soon as possible," Bondi said in the letter.
Bondi is a close ally of Italian prime minister Silvio Berlusconi and is a national coordinator of his ruling conservative People of Freedom party.