The vast majority of the communications (3,227) were supportive of Mr Bercow’s attack on the US president, while 854 opposed his position, figures released in response to a freedom of information request reveal.
The intervention sparked criticism from Tory MPs, who questioned whether the Speaker was complying with impartiality rules.
His position has since come under increasing threat after a video emerged of him telling students that he voted Remain in last year’s EU referendum.
Tory former minister James Duddridge has tabled a “no confidence” motion in Mr Bercow and has claimed that no Cabinet ministers are likely to support the Speaker in any vote.
Mr Duddridge said new supporters for the no-confidence motion had come forward after Conservative MP for Lincoln Karl McCartney sent out an email to all MPs on Tuesday.
Downing Street has said Mr Bercow’s future is a “matter for MPs”, in a sign that ministers will not be whipped into a position in any vote of no confidence.
Parliament’s website says the Commons Speaker “must remain politically impartial at all times”.