Former Lib Dem chief executive Lord Rennard has said he received no complaints about his behaviour during 27 years in the party.
Several women have come forward to accuse him of inappropriately touching and propositioning female party workers.
A new statement issued on his behalf said he "refutes" the allegations and will "co-operate with any properly constituted inquiry".
It added: "He would reiterate that in 27 years of working for the Liberal Democrats he received no complaint or allegation about his behaviour.
"Nor is he aware of any personal complaints being made in the three-and-a-half years since he stood down as chief executive until last week."
However, senior party sources have told Sky News that Chief Secretary to the Treasury Danny Alexander stands by a statement saying he spoke to Lord Rennard about "concerns" in 2008.
Earlier Lib Dem leader Nick Clegg said the police must be allowed to do their job and insisted he would not provide a "running commentary" on the allegations.
Speaking outside his home in southwest London, he told Sky News: "I understand there are many people who appear to want to act as self-appointed detectives trying to piece together events that happened many years ago but the only way that we are going to get to the bottom of the truth ... is by allowing the two investigations that I established immediately after the Channel 4 broadcast to do their job and, indeed, to allow the police, whom we have now approached, to do their job as well.
"And in the meantime I cannot and my party cannot provide a running commentary on every shred of speculation about events which happened many years ago."
Lord Rennard's statement made no reference to the police's involvement.
Pressure continues to mount on the Lib Dem leader, with party president Tim Farron admitting it "screwed up" its response to the allegations.
After initial denials that he was aware of complaints made by a number of women about Lord Rennard, Mr Clegg confirmed on Sunday his office had heard "indirect and non-specific concerns" as far back as 2008 and had taken action at the time.
He said that Mr Alexander, then his chief of staff, had put the concerns to Lord Rennard who denied any inappropriate behaviour.
Responding to the police investigation, the party's deputy leader Simon Hughes told Sky News: "We don't want there to be any no-go areas. If there are things that are criminal they need to be pursued."
The Met Police confirmed its officers met with the Lib Dem officials.
A Scotland Yard spokesman said: "The meeting was held to assist with our inquiries to ascertain if any criminal activity has taken place. That work continues.
"It was agreed at the meeting that any internal misconduct matters would be referred back to the Liberal Democrat Party."
Chief executive Tim Gordon led the Lib Dem group at the meeting.
A party spokesman said: "It is important that people with information have the confidence to come forward and that their information is dealt with sensitively and appropriately."