"We'll trace them... that is very possible to do," ANCYL spokesperson Floyd Shivambu said in reaction to at least 12 Malema impersonators existing on the social networking site.
"We are sure, when they get exposed, you will see it is white people. Reactionary, right-wing, white people."
Asked how the tracing would be done, he replied: "We don't want to expose our strategy on how we will get them. But we will get them and we are going to report them to the police. It's fraud, this thing, it's unacceptable, it's against the law.
"We will also institute civil claims against them and sue them.
"It is white people who are doing this because white people have a problem with the ANC Youth League."
Shivambu said the youth league had contacted Twitter's head office in San Francisco to complain about the impersonators. He said the US Embassy in South Africa helped the league contact the Twitter office.
"They (Twitter) made a commitment that they will close all those freak accounts as soon as possible. We are waiting for that."
But the ANCYL would continue with its own "tracing" and report the offenders to the police, Shivambu said.
On Thursday afternoon, a search for Julius Malema on Twitter showed all 12 impersonators were still alive and well. Of the 12, six bear the picture of the firebrand youth leader.
The last post by one of them, JuliusMalema82 said: "Eish mamma... wot is all this about us wanting to close Twitter. These bloody agents again."
Twitter users were in stitches on the site on Thursday morning following the news Malema wanted to close it down.
Tweets roll in
Tweets kept rolling in by the minute, with international news websites such as the BBC also picking up on the story.
"Julius Malema wants to shut down Twitter? Hahahahahahahahahaha, best joke4 2day," a user commented in reply to a post by 5fm radio jock Gareth Cliff.
Another, user EarleneBSmith, said: "Today is create a juju malema account day... do it... you know your red sockes (sic) want to... lol!"
Garethdv added: "ANCYL to close down Twitter... They truly are a bunch of gifted individuals!"
Another, kerryannerogers, pointed out grammar mistakes in the ANCYL statement: "In fact ANCYL statement called for 'closer of Twitter' following 'cretation' of fake accounts. Was that so we'd know it was the real Malema?"
The impersonators continued their work on Thursday morning.
One user, named JujuMalemaOZ, offered black empowerment "tips".
"Julius Malema empowerment tips#10 Friends = comrades, badguys = Agents, opposition = cockroach and Jonny walker (sic) = yebo yes!
"Julius Malema empowering tips#9 Agents are everywhere, use a helmet to block brain scanners, no need for me, no brain to scan," the post read.
Another impersonator, called julius_m_jnr, wrote: "Trying to help Daddy find the Pedi word for 'satire'... Any help plz, how do I explain it to him? #malema."
Someone else suggested: "Funny we may just have found the ANCYL's weak spot. They're terrified of Twitter. Let's all start fake Julius Malema accounts!"