Malema told reporters that Zuma confronted him after his speech at a rally near Bloemfontein on Youth Day, where Malema had said "we are prepared to take up arms and kill for Zuma".
"The president of the ANC said to me: 'That was a heavy statement' and I had to provide some explanation ... the president was shaken by the statement," Malema said at a media briefing in Johannesburg.
He then explained to Zuma that "we have no intention to kill whatsoever". "We never meant literally that people should be killed. We never called on anybody to immediately take up arms."
Asked whether he would apologise for the statement, as had been requested by the SA Human Rights Commission (SAHRC), Malema replied: "Why do you apologise for something you did not mean?"
However, Malema did say that he would never use the word "kill" in a speech again and that he would rather find a "creative way to say 'I will do anything to protect comrade Zuma' ".
"I will say... 'I'm prepared to pay the highest price on earth for Comrade Zuma', I will say that next time."
Malema accused the media of blowing his statement out of proportion "with a clear malicious intent and consequence".
"We have noticed the distortions, misinterpretations, vulgar insults and defamatory comments which have been hurled against the ANC Youth League.
Malema said it was all part of a political agenda to discredit the Youth League.
He said the Youth League would meet the national working committee of the ANC on Monday to further discuss the matter and that he had referred the SAHRC complaint for legal advice.
The SAHRC has given Malema 14 days to retract the remarks he made at the rally.
If Malema failed to respond, the commission would take the matter further "in line with its constitutional mandate", its spokesman Vincent Moaga said on Wednesday.
Meanwhile, the ANCYL in Limpopo has issued a statement of support for Malema.
"We wish to place it on record that the statement of taking up in arms in defence of comrade Zuma, was meant figuratively and not literally as an expression of the feelings of the ANCYL members," said acting provincial secretary Mitileni Goodman.
"We are fully behind our president and wish to call upon the public and interested parties to understand the context within which the case of the ANC president is being handled," Goodman said in a statement.