Cambridge Analytica, the firm involved in a row over its use of Facebook data, has suspended its boss Alexander Nix.
The chief executive’s comments, secretly recorded by Channel 4 News, “do not represent the values or operations of the firm,” it said.
In news reports shown on Monday, Mr Nix suggested tactics his company could use to discredit politicians online.
However, Cambridge Analytica said the report had “grossly misrepresented” the conversations caught on camera.
The London-based firm, along with the social network, is under scrutiny following claims by a whistleblower, Christopher Wylie, who worked with Cambridge Analytica.
He alleges it amassed large amounts of data through a personality quiz on Facebook called This is Your Digital Life.
He claims that 270,000 people took the quiz, but the data of some 50 million users, mainly in the US, was harvested without their explicit consent via their friend networks.
Mr Wylie says that data was sold to Cambridge Analytica, which then used it to psychologically profile people and deliver pro-Trump material to them, with a view to influencing the outcome of the 2016 presidential election.
Further filming by Channel 4 News, broadcast on Tuesday, showed Mr Nix claiming his firm had run Mr Trump’s digital campaign.
He said that the work the company did, including research, analytics and targeted campaigning, allowed the Republican candidate to win with a narrow margin of “40,000 votes” in three states.
The managing director of Cambridge Analytica’s political division, Mark Turnbull, was also shown telling undercover reporters that the company could create proxy organisations to spread negative material about opposition candidates online without being traced.
“We just put information into the bloodstream to the internet and then watch it grow, give it a little push every now and again over time to watch it take shape,” he said.
“And so this stuff infiltrates the online community and expands but with no branding – so it’s un-attributable, un-trackable.”
A statement from Cambridge Analytica’s board of directors said Mr Nix had been suspended with “immediate effect, pending a full, independent investigation”.
It added: “In the view of the board, Mr Nix’s recent comments secretly recorded by Channel 4 and other allegations do not represent the values or operations of the firm and his suspension reflects the seriousness with which we view this violation.”
The firm’s chief data officer, Dr Alexander Tayler – who was also filmed discussing campaign strategy for Mr Trump – will serve as acting CEO.