With the prospect of a hung parliament still looming, Shorten said that Turnbull should resign because he cannot command his own party and the voters have concluded he is "out of touch".
"This is farcical. Turnbull clearly doesn't know what he is doing. Quite frankly I think he should quit," Shorten, 49, said.
He likened Turnbull to the outgoing British Prime Minister, Cameron, who found himself on the wrong side of the Brexit result.
"He leads a divided party, he has had an election and he has delivered an inferior and unstable outcome."
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"He has taken this nation to an election on the basis of stability. He has delivered instability.
"His own party know he is not up to the job, the Australian people know he is out of touch and he has given a Senate reform which involves two or three One Nation senators."
Media report said that Shorten said the prime minister had made a bad situation worse with Senate reforms.
Shorten upped the ante against 61-year-old Turnbull as the poor election showing continue within the Coalition, and Nick Xenophon is positioning himself as the new parliamentary kingmaker.
According to the latest update from Australian Electoral Commission, Labor stood at 71 seats while Turnbull-led Liberal/National Coalition has 67. Counting will resume tomorrow.