In his statement, Malema said he had called Ramaphosa to apologise personally.
"After a long discussion with my wife about the president's apology, I have decided to pen down the apology that I should have communicated on the plaform of the joint sitting of parliament where it belonged," he said.
Malema said if there should be evidence produced to dispute his claim that he had never laid a hand on his wife or any other woman, he would be prepared to resign as an MP and president of EFF.
"I therefore, hope that this puts the matter behind both of us," he said. "I also would like to apologise to all South Africans who were offended in the process, in particular victims of gender-based violence."
However, the president also responded to claims by Malema - made on Tuesday during the first day of Sona debate - that Ramaphosa was a wife-beater. He said that Malema first raised this about three years ago. "He raised it in 2017 and said that the president used to assault his first wife, Hope Ramaphosa. Now, Hope Ramaphosa responded and said that is not true.
"You have raised the issue of my late former wife Nomazizi. She is not here to respond for herself," he said.
Ramaphosa said he had received a text message from a young woman who was upset at how gender-based violence was used as a political tool. "We should not resort to using issues such as these, as it was used also against you, to politicise and to trivialise an important issue that affects so many women in our country," he said.
"All of us need to engage in this struggle against GBV.
"I want to say, I am a father of daughters, I am a grandfather of granddaughters, I am a husband, I am a brother to a sister, and I also have 50% of the people in the cabinet who are women, and we also have South Africans, the majority of whom are women - and these are the people all of us must stand up and engage in the fight against GBV in our lifetime. "As we do it, we must have respect for one another and show respect for the women of our country," he said.
*Mamabolo could not be reached for comment.