Julian Smith has not denied ordering Tory MPs to ignore “pairing” arrangements – designed to help sick or pregnant MPs to miss votes – sparking calls for his resignation.
Quizzed on the controversy in Belfast, the prime minister was asked why she had not sacked him for “effectively trying to steal votes from the opposition”.
A Tory backbencher said Mr Smith all but admitted to her that he issued the order, which led to Brandon Lewis, the party chairman, voting when he was “paired” not to.
But Ms May replied: “There was an honest mistake made for which the chief whip and, indeed, Brandon Lewis have both apologised.”
The prime minister did not respond to the questioner enquiring if she “endorsed his conduct”, amid questions about how much she knew in advance of the votes.
An answer she gave to MPs on Wednesday appeared to imply that an “error” was made only in relation to Mr Lewis, whose “pair” was Liberal Democrat MP Jo Swinson, a new mother.
Since then, five MPs are reported to have said they were asked to abandon pairing arrangements before a vote on the EU customs union on Tuesday night – which the government won by just six votes.
The others ignored the instruction, after further advice, but Mr Lewis did break his pair – accidentally he has insisted.
In Belfast, after a one sentence answer about the row, a clearly uncomfortable Ms May immediately switched to talking about her Chequers plans to break the Brexit deadlock.
Labour said her response defied belief, calling for Mr Lewis and Mr Smith to resign and for the prime minister to “find the strength to sack them” if they refused.
“It is unbelievable that the prime minister has repeated the desperate and blatantly untrue excuses made by her party chair and chief whip,” said Tom Watson, Labour’s deputy leader.
“This is about public trust in politics. At such a crucial time for our country, people expect candour and decency, not cowardice and dishonesty.”
On Thursday, Heidi Allen, a Tory backbencher, said Mr Smith was “unable to confirm to me that he did not give instructions to break pairs”.
“Therefore I can only conclude MPs were told to break pairs on Tuesday,” she said. “I refuse to be tarnished by this behaviour so will not stand by and say nothing.”
Mr Smith is also believed to have admitted to a rival chief whip that he told Mr Lewis to break his pair – apologising only because he didn’t realise it was with someone on maternity leave.
Pairing allows MPs on different sides to agree not to vote so that absences for a variety of reasons – also including travel away from Westminster – do not change the margin of results of votes.
The positions of both Mr Smith and Mr Lewis appear safe while No 10 – following a rash of cabinet resignations – is determined to stand by them.
However, the chief whip will continue to face pressure to end his silence and explain what happened when MPs return to the Commons on Monday.