Facebook boss Mark Zuckerberg's decision not to appear before MPs is "astonishing", said the committee chairman who invited him to attend.
Damian Collins, the head of a parliamentary inquiry into fake news, urged Mr Zuckerberg to "think again".
Facebook and data analytics firm Cambridge Analytica are at the centre of a row over harvesting personal data.
Mr Zuckerberg has apologised for a "breach of trust", but said he will not appear in front of the inquiry.
He will instead send one of his senior executives, Facebook's chief product officer Chris Cox, who will give evidence to MPs in the first week after the Easter parliamentary break.
Mr Collins, the chairman of the Department for Culture Media and Sport select committee, said: "Given the extraordinary evidence that we've heard so far today... it is absolutely astonishing that Mark Zuckerberg is not prepared to submit himself to questioning.
"These are questions of a fundamental importance and concern to Facebook users, as well as to our inquiry as well.
"I would certainly urge him to think again if he has any care for people that use his company's services."
Facebook said Mr Cox was "well placed to answer the committee's questions".
At the weekend Mr Zuckerberg took out full-page advertisements in several UK and US Sunday newspapers to apologise, adding the company could have done more to stop millions of users having their data exploited by Cambridge Analytica.
The select committee on Tuesday heard from former Cambridge Analytica employee Christopher Wylie, who claimed the UK may not have voted for Brexit had it not been for "cheating" by the Leave campaign.
Mr Wylie told the committee that Canadian company Aggregate IQ - which has been linked to Cambridge Analytica - received funding from Vote Leave and played a "very significant role" in the referendum result.
He also claimed:
- His predecessor died in suspicious circumstances in a hotel in Kenya after a "deal went sour"
- Vote Leave and other pro-Brexit groups were working together and had a "common plan" to get round spending controls
- Cambridge Analytica worked for Brexit group Leave.EU and its "franchise", Aggregate IQ, was hired by Vote Leave
- The data Aggregate IQ possessed was used to target between five and seven million people during the referendum campaign
- Aggregate IQ said it had a "conversion rate" of 5-7% in persuading people to vote a specific way
Mr Wylie, whose allegations were first published in the Observer newspaper over a week ago, has accused Cambridge Analytica of gathering the details of 50 million users on Facebook through a personality quiz in 2014.
He alleges that because 270,000 people took the quiz, the data of some 50 million users, mainly in the US, was harvested without their explicit consent via their friend networks.
Mr Wylie claims the data was sold to Cambridge Analytica, which then used it to psychologically profile people and deliver pro-Donald Trump material to them to assist the presidential election campaign.
He described his former boss, Cambridge Analytica's CEO Alexander Nix, as a salesman with no background in politics or technology but a lot of wealth.
On one occasion, the two of them were running late because Mr Nix had to "pick up a £200,000 chandelier", MPs heard.
Cambridge Analytica claimed Mr Wylie "misrepresented himself and the company" to the committee.
It described him as a "part-time contractor" who left the firm in July 2014 after less than a year working there.
Mr Wyllie "had no direct knowledge of the company's work or practices since that date", it said.
Cambridge Analytica also said it was "disgusted" by his "use" of the "tragic death of a member of our team as a means to further his own agenda".
"An investigation by Kenyan authorities concluded that there was nothing suspicious about our colleague's death, and we as a company were deeply saddened by the loss," it said.
Cambridge Analytica also denies any of the data acquired was used as part of the services it provided to the Trump campaign.
Lawyers for Aggregate IQ have said the firm had "never entered into a contract with Cambridge Analytica" and it had "never knowingly been involved in any illegal activity".
Vote Leave has denied accusations that they broke the spending rules during the UK's 2016 referendum on whether or not to stay in the European Union.
In a blog on Friday, Vote Leave's Dominic Cummings said the claims were "factually wrong" and the Electoral Commission had approved donations in the run-up to the referendum.