The level of anger among Remain voters over Brexit should not be under-estimated, Sir Vince Cable has said.
The Lib Dem leader told the BBC that young people felt their future had been "taken away from them by a very narrow majority" in the 2016 referendum.
He suggested the Lib Dems would be "snapping at the heels" of the Brexit Party in Thursday's European election.
He conceded austerity cuts imposed by the Lib Dem-Tory coalition after 2010 contributed to the Brexit result.
"It was painful and unpleasant and there were political consequences," he said of decisions by that coalition government to cut public spending.
The Lib Dems are one of several parties contesting Thursday's elections which want the UK to remain in the EU.
Sir Vince said, while it was unfortunate that pro-Remain parties were competing against each other for votes, he expected the total number of those votes to end up "roughly similar" to that won by the Brexit Party and UKIP.
He said he expected the Lib Dems to get more votes than either Labour or the Conservatives and run Nigel Farage's Brexit Party a close second.
Sir Vince said the country was "bitterly divided" and, while he acknowledged the frustration of those who voted to leave the EU, he said those who wanted to remain were also rightly dismayed about the current situation.
"I understand how angry people are on both sides. There are some angry Leavers and there are some very angry Remainers too, particularly young people who feel their future has been taken away from them on the basis of a very narrow majority, where a significant majority of the electorate did not vote and many young people did not get an opportunity to vote."
The way to resolve the current stalemate, he suggested, would be to ask the public to confirm whether they still wanted to leave in another public vote.
This would not be a rerun of the 2016 referendum, he insisted, because the country was in a "totally different place" to three years ago.
"I'm afraid the referendum resolved nothing and we do have to go back to the people and ask if what is now on offer is what they really voted for.
"We have got completely different views about what Brexit actually means. What has emerged over the last three years is that the prospectus on which the Leave vote was achieved was based on a tissue of lies to be frank."
He said he was confident the public would vote to stay in the EU in another referendum and he would not be joining calls, at this stage, to stop Brexit in its tracks by revoking Article 50, which he described as the "extreme, nuclear option".
Sir Vince said he would be leaving the party in a strong position when he steps down as leader after the European elections.
"We are a major national political force again and will be when the general election comes around."