Chief whip Julian Smith is under mounting pressure to resign, amid reports he told MPs to renege on agreements not to vote during knife-edge Brexit divisions.
Mr Smith apologised when it was revealed Conservative Party chairman Brandon Lewis broke a "pairing" agreement with Lib Dem deputy leader Jo Swinson.
Under House of Commons tradition, an MP from one party who is unable to attend a parliamentary vote can ask for a "pair" from another party, an agreement that sees one of their MPs also miss the vote.
Ms Swinson, who recently gave birth to her son Gabriel, reacted furiously when Mr Lewis was revealed to have voted in two close divisions on the Trade Bill on Tuesday.
Mr Lewis' participation in the votes did not affect the outcome, but the breach of tradition has provoked anger without and within the Tories.
Mr Lewis said it was an "honest mistake", while Mr Smith said sorry and claimed the Tory party chair had been "asked to vote in error".
But according to The Times, Mr Lewis and two other MPs were told by Mr Smith that they should vote, despite being paired.
The two unnamed MPs ignored the instruction after seeking further advice, the newspaper reported.
In response, a Conservative spokesman did not deny the main thrust of the story - that Mr Smith told MPs to break their "pairing" arrangements.
"We have apologised for the fact that a pregnancy pairing arrangement was broken in error this week," he said.
"No other pairs offered on the Trade Bill on Tuesday were broken."
Reacting to the report, Ms Swinson said: "Well... This reflects pretty badly on those peddling the 'honest mistake' nonsense.
"To be fair, hats off to the two MPs who told their chief whip to take a running jump when he asked them to break a pairing just because the govt might lose.
"We still need proxy voting."
Tory MP Heidi Allen also raised her concerns.
There are currently no formal maternity or paternity arrangements in Parliament, with informal leave arranged at party level.
Senior Labour MP Harriet Harman is leading current efforts for MPs to be given six months' maternity leave, with provisions for colleagues to vote on their behalf during their absence.
Theresa May was asked about the furore during Prime Minister's Questions, telling MPs: "The breaking of the pair was done in error.
"It wasn't good enough and will not be repeated."
The PM still has full confidence in Mr Smith, according to Downing Street.
Mrs May's official spokeswoman also said the PM stands by her comments about the pact being broken in error.
Labour has called for the chief whip and party chairman to resign or be sacked.
"The Tories' story is changing by the minute as they desperately scramble to cover up their appalling actions," said Labour Party chair Ian Lavery.
"This Government is rotten to its core.
"Julian Smith and Brandon Lewis must now resign or be sacked, and Theresa May must apologise for misleading the House."
The Lib Dems have called for Mr Smith to make a statement in Parliament and "be accountable for this mess".