Mr Smith, who will on Friday formally launch his bid to be leader, said on Thursday that if he got the job he would push for an early election or another referendum.
The move echoes a promise by Tim Farron, leader of the Liberal Democrats, who has said his party will pledge in its election manifesto to derail Brexit.
Mr Smith said he respected the decision of those who had voted “in good faith” to leave the EU. But the Pontypridd MP had encountered many who regretted their decision and were upset over being “clearly misled” by the Leave campaign.
“That does mean a second referendum or a general election when the terms are clear. The Labour government should be committing to that,” he told the Guardian.
His position is markedly more enthusiastic about the EU than that of Mr Corbyn, who gave halfhearted support to the Remain side.
Mr Smith, former shadow work and pensions secretary, announced on Wednesday that he would stand against Mr Corbyn in the race sparked by a leadership challenge by Angela Eagle earlier in the week.
The Welsh MP said that either Ms Eagle or he ought to stand aside, depending on support, to create a “unity candidate” to challenge the incumbent. “Ideally, we would have one candidate, and the clarity of that one candidate, versus Jeremy Corbyn,” he said.
But Ms Eagle has not agreed to make way if she secures the support of fewer MPs than her rival. “I will leave Owen to do his own thing, I’ll do my own thing,” she said this week.
An attempt to thwart Mr Corbyn by forcing him to gain the backing of 51 MPs to go on the ballot sheet failed on Tuesday when a meeting of the party’s National Executive Committee ruled in his favour.
Allies of Mr Corbyn are discussing how to oust Iain McNicol, the party’s general secretary, for his involvement in the NEC meeting.
It emerged on Thursday that a Labour donor was planning to mount a legal challenge against the NEC for its decision. Michael Foster, a former parliamentary candidate, will lodge the application at the High Court on Thursday afternoon.
“The issue raised by my application to the court is the proper interpretation of the rules of the party,” he told BBC Radio 4’s Today programme, saying the matter was “essentially a legal issue”.
The challenge has been criticised by the Corbyn team and his opponents in the Parliamentary Labour party. Tom Watson, deputy leader and one of the few remaining moderates in the shadow cabinet, called it “unhelpful and destabilising” to the party.
“The NEC made a decision. They ruled that Jeremy Corbyn is automatically on the ballot paper,” he said. “We must respect that decision and give our members a choice of candidates as soon as possible.”
Mr Foster, a former show business agent and member of Labour Friends of Israel, has given the party more than £400,000 since 2010.
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