Mr Shorten tabled documents from the UK Home Office confirming he renounced UK citizenship prior to his election in 2007.
But in tabling the letter, he warned that MPs and Senators should not be forced to provide such proof from “baseless” allegations.
“I accept that, if I want to be elected prime minister, there cannot be any doubt about my constitutional eligibility pushed by the conspiracy theorists like the prime minister and the member for Warringah,” he told the House of Representatives shortly after Question Time.
It follows for Mr Shorten to release documentary evidence of his proof of renunciation of British citizenship.
Mr Shorten said he offered the proof to the parliament to put an end to “baseless allegations, not reward them”.
“I will not allow the prime minister use the smear about me as cover for the crisis which engulfs his government. This silly distraction has to end, the circus has to stop,” he declared.
“I strongly believe that MPs and senators should not be forced to provide evidence to counter claims that are made completely without evidence. No matter which party they are from.”
He said this was a chance to draw a line in the sand.
“In an age of Twitter trolls, baseless online conspiracy this is a chance for parliament to declare we are bigger and better than this.
“To accept otherwise, to turn our back on the notion that a person making the allegation must have some evidence, sets a dangerous precedent.”
Earlier, Mr Abbott challenged Mr Shorten to "show it or shut up" on his renunciation documents.
"Because if you haven't got a letter, you are in exactly the same position that he is in and you should let him and you should let the Parliament get on with its job this week," the Warringah MP said.
Mr Turnbull also heaped pressure on Mr Shorten to produce documents, demanding proof.
"What is he trying to cover up?" the Prime Minister asked.
Liberal MP Ann Sudmalis, who had previously stated she would produce proof she is not a UK citizen if Mr Shorten did so first, tweeted her documents.