The chief executive of the social media giant said he had “personally asked one of his deputies” to attend and give evidence to the Digital, Culture, Media and Sport Committee in its inquiry.
The tech giant and data analytics firm Cambridge Analytica are at the centre of a dispute over harvesting personal data and whether it was used in Donald Trump’s US presidential election campaign.
Mr Zuckerberg has apologised for a “breach of trust”.
He took out full-page advertisements in several UK and US Sunday newspapers to apologise over the weekend.
In a letter to committee chairman Damian Collins, Facebook’s head of public policy Rebecca Stimson said despite a request Mr Zuckerberg attend in person, the company would be putting forward chief technology officer Mike Schroepfer or chief product officer Chris Cox.
She said both Mr Schroepfer and Mr Cox “report directly to Mr Zuckerberg and are among the longest serving senior representatives in Facebook’s 15-year history”.
“Both of them have extensive expertise in these issues and are well placed to answer the committee’s questions on these complex subjects,” the letter said.
One of the two men could appear before the inquiry straight after the Easter Parliamentary recess, which ends on 16 April.
Mr Collins repeated his call for Mr Zuckerberg to give evidence to its inquiry into fake news, saying it would be “appropriate” for him to do so in person or via video link.
In a statement at the opening of the committee hearing, the chairman said: “We believe, given the serious nature of the allegations that have been made around the access and use of Facebook user data, that it is appropriate that Mark Zuckerberg should give evidence to the committee.
“He has suggested that Chris Cox, the chief product officer at Facebook, could come to London to give evidence to the committee in the first week after the Easter recess.
“So we would be very happy to invite Mr Cox to give evidence. However we would still like to hear from Mr Zuckerberg as well.
“We will seek to clarify from Facebook whether he is available to give evidence or not, because that wasn’t clear from our correspondence.
“If he is available to give evidence then we would be happy to do that either in person or by video link, if that would be more convenient for him.”