The House of Commons petitions committee is investigating allegations of fraud in connection with a petition calling for a second EU referendum.
Its inquiry is focused on the possibility that some names could be fraudulent - 77,000 signatures have already been removed.
More than 3.2 million signatures are on the petition, but PM David Cameron has said there will be no second vote.
The UK voted by 52% to 48% to leave the EU in Thursday's referendum.
Helen Jones, who chairs the cross-party petitions committee, said in a statement posted on Twitter that it was taking the allegations "very seriously".
'A range of views'
"People adding fraudulent signatures to this petition should know that they undermine the cause they pretend to support," she said.
The committee will consider the petition at its meeting next week and decide whether to schedule a debate on it, Ms Jones said.
"That doesn't mean that the committee will be deciding whether or not it agrees with the petition - just whether or not it should be debated.
"Any debate would allow a range of views to be expressed."
A number of people on Twitter have pointed out that some people appear to have signed the petition from outside the UK.
Only British citizens or UK residents are permitted to sign the petition, including Britons based abroad.
The House of Commons petitions committee said it will continue to monitor the petition for "suspicious activity".
The petition has more signatures than any other on the parliamentary website.
A House of Commons spokeswoman said the petition was created on 24 May. There were 22 signatures on it at the time the referendum result was announced.
The petition's website states it was set up by an individual called William Oliver Healey, and says: "We the undersigned call upon HM Government to implement a rule that if the Remain or Leave vote is less than 60%, based [on] a turnout less than 75%, there should be another referendum."
Thursday saw a 72.2% turnout, significantly higher than the 66.1% turnout at last year's general election, but below the 75% mark suggested by Mr Healey as a threshold.
In a statement posted on Facebook, a campaigner for the English Democrats party identifying himself as Oliver Healey says he started the petition "when it was looking unlikely that 'leave' were going to win, with the intention of making it harder for 'remain' to further shackle us to the EU".
He says the petition has since been "hijacked by the remain campaign".
BBC political correspondent Iain Watson says the petition has attracted a lot of attention but has no chance of being enacted, because it is asking for retrospective legislation.
Our correspondent says some referendums do have thresholds but those clauses must be inserted in legislation before the vote so everyone is clear about the rules.
You cannot simply invent new hurdles if you are on the losing side, our correspondent says.
Mr Cameron said on Friday he would stand down as prime minister by October following the leave result.