Democratic Alliance (DA) leader Helen Zille has asked for an urgent meeting with President Jacob Zuma to discuss "the implications of [African National Congress Youth League (ANCYL) president] Julius Malema's hate speech".

A written request for a meeting was sent to the President's office on Tuesday, her office said in a statement.

Earlier, Zille addressed the media at Parliament on the murder at the weekend of Afrikaner Weerstandsbeweging (AWB) leader Eugene Terre'Blanche and Malema's use of a struggle song that includes the words "shoot the boer".

She told journalists that merely pointing out, as the ANC had done, that there was no direct evidence linking Malema's hate speech to Terre'Blanche's murder was "unhelpful, to say the least".

Zille also called on Zuma to "act like a President and tell his youth league and its leader that we cannot allow our history of division to destroy our chances of building a shared future".

Responding to a question, she said that Malema's use of a provocative struggle song had not come out of nowhere.

"When we have a leader who sings "bring me my machine gun", what's the machine gun for? Not eating your breakfast. That's the critical point; these things all go together.

"Struggle songs are part of our history, but then there are very different struggle songs as well, that don't contain those words."

For a leader to sing a song about "bring me my machine gun" was totally inappropriate in a constitutional democracy.

Zille warned that Malema was prepared to sacrifice South Africa's future to further his own ambitions.

He had no concept of the rule of just law and due process, and no understanding of the constitution, for which many had worked and were seeking to defend.

"[He] believes that in his personal, political interest he can undermine everything everybody has fought for, for so long, and sacrifice everyone's future for the sake of his personal ambitions. That is what we're dealing with here.

"Julius Malema occupies no position at any level of government... Yet somehow he manages to drag everybody else in that government around by the nose," she said.

It was crucially important for Zuma to take a hard line with extremists such as Malema, but he had not done so.

"He's missed opportunity after opportunity, and he lets us conclude only one thing: that Julius Malema has some sort of hold over Jacob Zuma that makes it impossible for Jacob Zuma to do his duty as the country's president," Zille said.