Heidi Allen, a Tory backbencher, said she “hoped” the allegations were untrue and warned of the importance of “integrity and standards”.
Opposition MPs said Mr Smith would have to resign if the claims were true.
Jacqui Smith, a former Labour chief whip, tweeted: “If your word stands for nothing… you can’t be a Chief Whip… Needs to go now.”
Yesterday’s Evening Standard quoted a Commons source as saying Mr Smith put “undue pressure” on MPs to break pairing rules — where MPs on each side agree not to vote — to secure the Government’s narrow six-vote victory in a vote on the customs union.
Today’s Times said Mr Smith urged three Conservative MPs to breach pairing deals, where MPs on each side agree not to vote.
A spokesman for Mr Smith denied the allegations. He said: “We have apologised for the fact that a pregnancy pairing arrangement was broken in error this week. All other pairs offered on the Trade Bill on Tuesday were honoured.”
However, Liberal Democrat chief whip Alistair Carmichael demanded that Mr Smith make a Commons statement on the matter.
He said that despite receiving a private explanation from Mr Smith over how the pairing arrangement between Tory party chairman Brandon Lewis and Lib-Dem Jo Swinson had been broken during two key Brexit votes on Tuesday night, he still was unclear how it exactly happened.
After the fresh allegations against Mr Smith, Ms Allen, a prominent anti-Brexit campaigner, said: “I sincerely hope this isn’t true. No matter how tough the going gets, principle, integrity and standards matter. Without those, what’s left?”
Labour MP Chris Bryant said: “If this is true then the chief whip must resign. It’s a simple matter. Either his word is his bond or it isn’t.”
Theresa May admitted yesterday her party’s failure to honour the voting pact was not “good enough” but that it was an honest mistake.