MP Rob Roberts has been suspended for sexual misconduct, with a senior minister suggesting it would be "honourable" for him to stand down.
A motion to suspend the Delyn MP for six weeks was approved by the House of Commons after he breached sexual misconduct rules.
Mr Roberts, who was a Conservative MP, made repeated unwanted advances to a member of staff, for which he lost the Tory whip.
The North Wales MP's misconduct was "significant", a report found.
Despite no longer being able to represent the Conservative Party, recall laws mean he cannot face the prospect of losing his seat until the next election.
A petition to hold a by-election could only happen if sanctions were imposed on the recommendation of the Commons' Committee on Standards or another Commons committee, instead of by the Independent Complaints and Grievance Scheme, as in this case.
Prime Minister Boris Johnson, speaking before Mr Roberts was suspended, said he believed the MP had received "condign" (appropriate) punishment.
But Commons leader Jacob Rees-Mogg said: "Following a case of this severity in which it would be honourable for a member to stand down after the withdrawal of the whip, we need to look at whether the process is striking the right balance between the defendants, protecting the confidentiality of the complainants, and in ensuring consistent outcomes across different types of conduct case.
"I can therefore confirm to the House that I have asked the chairman of the independent expert panel for his views on whether changes should be made to the current process to enable recall to be triggered.
"In my view, any changes in this regard should be made in the most straightforward way possible and my preference would therefore be for a non-legislative solution."
He said it was "frankly ridiculous" that there are more serious sanctions for "somebody who uses a few envelopes incorrectly than for somebody who is involved in sexual misconduct".
Mr Rees-Mogg said it is ultimately for the House of Commons to make a decision.
Labour's shadow Commons leader Thangam Debbonaire said she agreed "non-legislative solutions" were needed, adding: "In what other job could someone who has carried out sexual misconduct not face losing that job?"
She offered to work with Mr Rees-Mogg to "close the loophole urgently and seek solutions".