Okonjo, who was held hostage for five days, was on Friday rescued from kidnappers' den in Delta State.
Okonjo-Iweala who spoke yesterday while briefing journalists on her mother's release said, "My mother suffered a great deal during this ordeal. It was only the Almighty God that rescued her from a situation that could easily have ended tragically.
"She said she was left without food and water for the five days in captivity and the kidnappers spent much of the time harassing her.
"They told her that I must get on the radio and television and announce my resignation.
"When she asked why, they told her it was because I did not pay oil subsidy money. They also said I had blocked payment of money to certain components of the SURE-P programme."
The minister, however, denied stopping payment of oil subsidy to those that deserve it.
She said, "These statements are, of course, not true. In the case of subsidy payments, we have been paying all marketers whose claims have been verified by the Aig-Imoukhuede Committee after going through the necessary processes.
"For marketers whose transactions are proven to be fraudulent, the position of the Jonathan government is also clear: we cannot and we will not pay. We will not back down on this. We will continue to stand firm.
"In the case of SURE-P, there is a totally different process that I have no control over. This is the right thing to do. And this, I believe is what the Nigerian people want."
The minister said she would have been jumping in jubilation for the release of her mother but that the death of Kaduna State Governor Patrick Yakowa and former National Security Adviser General Andrew Azazi in a helicopter crash on Saturday tampered with her mood.
When contacted to confirm the minster's claim, police spokesman Frank Mba said he was not aware of the minister's claim and would not talk on it. "I will not comment on that," he said.
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