The former work and pensions secretary in the shadow cabinet, who stepped down last month in a party coup against incumbent Jeremy Corbyn, claimed many of those who voted for the country to quit the European Union were misled by the Leave campaign.
"We should give them another chance. That does mean a second referendum or a general election when the terms are clear," Smith said.
UK's new Prime Minister Theresa May ruled out a new referendum earlier this week, saying that "Brexit means Brexit."
But Smith claimed that a lot of people were now angry that they had been "quite clearly misled" by the pro-Brexit campaign, specifically on where Britain's EU contributions would go.
The majority of British nationals voted to drop out of the 28-nation bloc in the June 23 referendum. Many of the senior Labour officials accused their leader Corbyn of a lackluster campaign to keep the country in and triggered an election process to challenge him.
