Lord Janner is alleged to have sexually abused children over a period spanning more than 30 years and dating back to the 1950s, a public inquiry has heard.
The late politician was said to have arranged for children "in whom he had a sexual interest" to be brought to the Houses of Parliament, the Press Association reported.
Allegations involving Janner, who died aged 87 in December, are being examined as part of the wide-ranging Independent Inquiry into Child Sexual Abuse, chaired by Justice Lowell Goddard.
Speaking at the first preliminary hearing, counsel to the inquiry Ben Emmerson QC said: "The allegations in summary are that Greville Janner exploited children and perpetrated a full range of sexual offences against them, including what would now be termed in English law as rape.
"In relation to a number of the complainants it is alleged that Janner abused his position as an MP by arranging for children in whom he had a sexual interest to be brought to the Houses of Parliament."
The alleged offending was said to have taken place at children's homes and hotels.
The period during which it is alleged Janner committed the offences is 1955 to 1988, the inquiry heard.
Director of Public Prosecutions Alison Saunders originally decided that the peer, who denied the allegations, should not be charged because he was suffering from dementia.
However, this was overturned by an independent review and, although Janner was unfit to stand trial, a proceeding called a trial of the facts was due to take place at the Old Bailey. This was abandoned when he died.
Emmerson said that, of more than 30 alleged victims who made contact with police, 12 had been selected to give evidence at trial.
Seventeen complainants have been given core participant status at the inquiry.
It is unable to determine criminal or civil liability, but Emmerson said it will "often be required to make findings of fact on allegations which, if true, may amount to the commission of a criminal offence".
He added: "No one should be in any doubt, therefore, that where the evidence justifies it...the panel will make findings of fact on allegations of child sexual abuse."
Emmerson said the inquiry has so far not received an application for core participant status from Janner's family. They have previously said he is "entirely innocent of any wrongdoing".
The inquiry will consider whether there were institutional failures to protect children, with bodies including Leicestershire County Council, the police and the Labour Party set to come under scrutiny.
The examination of claims linked to Janner is one of 13 investigations launched by the inquiry, which is set to last for five years and has a budget of £17.9million for this financial year.
An overarching investigation will also look into allegations of child sexual abuse and exploitation involving people of public prominence associated with Westminster.
Emmerson said: "Allegations of the involvement of politicians in child sexual abuse are reported, on the one hand, as evidence of a paedophile conspiracy at the heart of Westminster and, on the other hand, as evidence of a modern-day witch-hunt.
"It is the role of this inquiry to move from the realms of rumour and speculation, allegation and counter-allegation, to the assessment of objective facts."
He added that the inquiry "will also need to recognise the damage that can be caused by false accusations of sexual abuse, without hesitating to make findings against individuals and institutions if justified by the evidence".
Referring to the inquiry as a whole, Emmerson said: "The task is vast but critically important."
He cited figures indicating that between April 2012 and March 2014 more than 50,000 children were identified as victims of sexual abuse.
"These figures should answer the doubts of anyone who questions the need for this inquiry," Emmerson added.
The first full hearings in the Janner strand of the inquiry are expected to be held in September.