Labor wants SBS chairman Nihal Gupta to be sacked, for failing to answer questions over whether he lied to get the job.
The call came after Mr Gupta appeared before a Senate estimates hearing in Canberra on Thursday.
Labor senator Sam Dastyari repeatedly clashed with the chairman, who refused to answer questions about his appointment to the five year position, on an annual pay-packet of $120,000.
The chairman would not be drawn on whether he told a selection panel he had 200 employees at his company Digital Electronics Corporation Australia.
Subsequent reports in The Australian suggested it had no staff.
"You're kidding me, you can't even answer a simple question," Senator Dastyari replied, after Mr Gupta wouldn't say when he first heard about the chairmanship vacancy.
"This is a complete joke."
The senator said he had serious concerns the chairman gave false and misleading evidence to the panel.
Mr Gupta said he didn't believe he should have to come to the committee and "substantiate (his) appointment".
Following his appearance, Labor's communications spokesman Jason Clare said Malcolm Turnbull should sack Mr Gupta.
"If he doesn't the question needs to be asked, how can Malcolm Turnbull think he is up to running the country if he supports someone who clearly holds the Parliament in contempt," Mr Clare said in a statement.
Senator Dastyari also said he would attempt to launch a separate inquiry into Mr Gupta's appointment.
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