Trade Minister Craig Emerson told Fairfax on Wednesday that Ms Bishop should not stay on her post a minute longer following reports by the media firm that she spoke with Mr Blewitt and lied about it.
"If those media reports are correct, then Julie Bishop has out and out lied ... She should therefore resign or be sacked," Dr Emerson said.
However, in a statement issued by the Coalition number two, Ms Bishop clarified that she never initiated any contact with Mr Blewitt and the talk she had with the alleged bagman for former Australian Workers Union (AWU) boss Bruce Wilson was purely incidental.
Ms Bishop claimed she received a call from radio host Michael Smith last week and the phone was passed to a man she was not aware was Mr Blewitt.
"That person did not identify themselves and said he was pleased that the AWU fraud was being raised in parliament," Ms Bishop was reported by the Australian Associated Press (AAP) as saying in the statement.
The same Mr Smith, according to Fairfax, acted as the facilitator of the meet between the Coalition official and Mr Blewitt, which reportedly took place Friday last week and was denied by Ms Bishop.
Yet the details that the Liberal MP had provided was sketchy at best, according to Labor MP Yvette D'Ath, who scored Ms Bishop for leading the Coalition's 'muckraking' against Prime Minister Julia Gillard over the AWU slush fund controversy.
Ms Bishop needs to cease her demands for further explanation from Ms Gillard when the deputy opposition leader herself "can't even recall what she did last week," Ms D'Ath told The Sydney Morning Herald.
Meanwhile, Labor backbencher Steve Gibbons issued an apology over his Twitter post attacking the Coalition that says: "Libs are led by a gutless douche bag and a narcissistic bimbo who aren't fit to be MPs let alone PM and Deputy. Both should be sacked."
Mr Gibbons has since deleted the tweets but senior government minister Jenny Macklin labelled the quips as unnecessary.
"Nobody should use that language about other members of parliament," Ms Macklin told Sky News today.
Also, senior Labor minister Anthony Albanese has insisted that Ms Bishop has to provide more satisfactory answers in light of the conflicting conduct and statements being observed from her.
Mr Albanese had earlier declared that Ms Bishop's position is now untenable following the Coalition official's accusations that Ms Gillard acts while lawyer for AWU were tantamount to criminal conduct.