Mr Slipper has denied claims published in The Daily Telegraph that he sexually harassed a male staffer and misused Cabcharges.
The claims against Mr Slipper, made in court documents obtained by the newspaper, allege he recruited 33-year-old James Ashby for the sole purpose of pursuing a sexual relationship with him.
The application filed to the Federal Court says Mr Slipper allegedly made unwelcome advances toward Mr Ashby and sent him explicit text messages making his sexual intentions clear.
Mr Slipper took to Twitter early on Saturday morning to deny the claims. He is overseas on a parliamentary delegation.
"The allegations in News Ltd papers are denied!" he tweeted, later adding they were "a surprise to me".
Opposition Leader Tony Abbott said the Speaker's role was to uphold the integrity of parliament and Mr Slipper should step aside while the allegations were heard in court.
"Yes, the Speaker is entitled to the presumption of innocence but he does have quite a lot of explaining to do," he told reporters in Queensland on Saturday.
"These are matters that are now to be the subject of proceedings in court, so these are of a vastly more serious and substantial nature than anything that has been alleged against Mr Slipper in the past."
The Australian Federal Police said on Saturday they were aware of the new allegations that Mr Slipper misused taxpayer-funded Cabcharges.
A spokeswoman told AAP police were assessing the information they had about the allegations but it would not be appropriate to comment further at this stage.
Mr Slipper became Speaker on the last day of parliament in 2011 after the Labor speaker, Harry Jenkins, resigned.
The Sunshine Coast MP resigned from the Liberal National Party to take the job.
His defection effectively gave the minority Labor government two extra votes, a wider buffer than previously.
Prime Minister Julia Gillard has been contacted for comment on the allegations.
