The Pontypridd MP and former Shadow Work and Pensions Secretary said in an interview with The Guardian that the British electorate should be allowed a say after a new deal with the European Union was struck.
Mr Smith, who joined the race to challenge Jeremy Corbyn for the party leadership on Wednesday, said either he or fellow challenger Angela Eagle should stand aside, depending on support, to give a unity candidate a free run at the leader. "That does mean a second referendum or a general election when the terms are clear", Smith said. Eagle had told The Guardian that she supports a similar position on the referendum, agreeing that any Brexit deal should be followed by a second plebiscite or election.
He added: "I think there are many people out there who voted in good faith for Brexit and who felt they were doing the right thing for their families and their communities and I respect them for taking that decision". Numerous senior Labour officials accused their leader Corbyn of a lackluster campaign to keep the country in and triggered an election process to challenge him. A lot of people are angry that they were quite clearly misled by the Brexit campaign'.
Labour's ruling National Executive Committee said on Tuesday that Mr Corbyn would automatically go on to the ballot paper as the sitting leader.
Mr Smith said "ideally" there would only be one candidate facing Mr Corbyn in the contest, so that moderate MPs could rally around a single figure.
"I thought at the time the tradition of the Labour Party and the tradition of left-wing engagement to remove dictators was a noble, valuable tradition and one that in south Wales, from the Spanish civil war onwards, we have recognised and played a part in", he told the Western Mail.
'I must abide by them and so must the party.
'But, equally if it misapplies the rules, I am entitled to say that it has broken my contract of membership.
Former shadow business secretary Ms Eagle - who has already secured 51 nominations from MPs - has been calling for Mr Corbyn to resign for days.
And on the private finance initiative, he said: "I'm not someone, frankly, who gets terribly wound up about some of the ideological nuances".
"And finally, an inability that Jeremy has to have his parliamentary party convince him of anything - no reaching out, a pushing away".
"Let's wait and see where we end up".