The Ex-Welsh secretary has apologised for sending explicit texts to a woman he interviewed for a job in 2013 when she was 19-years-old.
The senior MP, who stood for the Conservative leadership last year, admitted to The Mail on Sunday that he had said "some pretty outrageous things" to the woman after meeting her, and that the messages "basically amount to unfaithfulness".
He said he had been "foolish" but insisted there he had no sexual contact with the teenager.
He went on to say: "We exchanged messages which talked about sex but none of it was meant seriously."
International trade minister Mark Garnier is accused of harassing a female aide.
The 53-year-old MP for Wyre Forest said he was "not going to be dishonest" and admitted to asking his Commons Secretary Caroline Edmondson to buy sex toys for him.
However, the father of three strongly denies the harassment claim, and described the incidents as "good-humoured high jinks" and "amusing conversation".
The report comes after Downing Street warned on Friday that Theresa May would take "serious action" against any minister found to have acted inappropriately.
A list of 13 MPs facing harassment allegations has been circulating at Westminster, according to The Daily Telegraph and the Prime Minister ordered a Cabinet Office inquiry into whether Mr Garnier breached the ministerial code.
The Guido Fawkes website has reported 36 serving Conservative MPs have allegedly been accused of inappropriate behaviour.
It listed their claimed misdemeanors, including "handsy with women", and "inappropriate with male researchers".
Theresa May is offering to hold talks with Speaker John Bercow on overhauling Commons disciplinary procedures amid the mounting reports of abusive and inappropriate behaviour towards women.
In a letter to Mr Bercow, the Prime Minister said the current grievance system for dealing with complaints by MPs' staff lacked "teeth" as there was no contractual requirement for MPs to follow its procedures.
She added: "I do not believe that this situation can be tolerated any longer. It is simply not fair on staff, many of whom are young and in their first job post-education," she wrote.
"It is vital that the staff and the public have confidence in Parliament and resolving this employment irregularity on a cross-party basis can play an important role in this.
Labour MP Jess Phillips has called on Mrs May to suspend Mr Crabb from the Conservative Party pending an investigation into his conduct.
Writing in The Times Red Box email, she said: "Theresa May must put her money where her mouth is and investigate Stephen Crabb while his whip is removed."