A woman who told police she was raped by a former Conservative minister complained about his behaviour to a senior party figure four months ago.
It is understood that Tory chief whip Mark Spencer spoke with the complainant in April, but Mr Spencer insists she did not make any allegation of serious sexual assault.
The party said it will not suspend the MP while investigations are ongoing.
The MP, in his 50s, was arrested on Saturday and has since been bailed.
The Metropolitan Police said the allegations related to four separate incidents claimed to have taken place between July 2019 and January 2020.
The Sunday Times reported that the allegations against the former minister had been made by an ex-parliamentary employee.
A spokesman for the chief whip said that he took all accusations of harassment and abuse extremely seriously and had strongly encouraged anybody who has approached him to contact the appropriate authorities.
According to sources, Mr Spencer had not known the “magnitude” of the allegations.
But a report in the Daily Telegraph suggested the woman became frustrated after they spoke that nothing was done.
It is also understood the Leader of the House of Commons, Jacob Rees-Mogg, was told by an MP in recent weeks about the claims – with sources saying he had said the woman should contact the police.
The decision not to remove the whip – which effectively expels members from the party – has been criticised by Labour’s Jess Phillips, who said the decision was “shocking” and sent a “terrible message from Westminster”.
A spokesman for the Conservative Party whips’ office said: “The whip has not been suspended. This decision will be reviewed once the police investigation has been concluded.”
This means he can continue to sit in the House of Commons as a Conservative.
Business Minister Nadim Zahawi told BBC Breakfast that the allegations were “very serious”.
“There is a police investigation taking place. It is only right that we wait for that investigation to conclude before hearing from the chief whip as to the action the Conservative party will take.
“I think it is wrong to speculate before we see the police investigation completed”, he said.
The Sunday Times, which first reported the story, said the complainant alleges that the MP assaulted her, forced her to have sex and left her so traumatised that she had to go to hospital.
The Metropolitan Police said it had launched an investigation into the allegations.
“On Friday, 31 July, the Metropolitan Police Service received allegations relating to four separate incidents involving allegations of sexual offences and assault,” the force said in a statement.
“These offences are alleged to have occurred at addresses in Westminster, Lambeth and Hackney between July 2019 and January 2020.”
Police said the man has been released on bail to return on a date in mid-August.