Speaking to the Press Association after the resignation of two of his frontbench MSPs - close ally Neil Findlay and Justice Secretary Daniel Johnson - the Scottish Labour leader said the "change in circumstances" following the elections had led him to conclude a confirmatory vote must be held.
A policy change will be voted on when Labour's Scottish executive committee meets on Saturday June 8, a party spokeswoman confirmed.
That came after MSPs at Holyrood had their second group meeting of the day, where there were "frank and honest" discussions in the wake of the party's poor performance in the recent European elections.
A decision to not only support a second Brexit referendum, but to campaign for Remain in such a vote, could be take regardless of what UK Labour's policy is.
"If there is a second vote then not only will we back Remain but Richard will publicly campaign for it," the spokeswoman said.
Mr Leonard insisted he had the support of his parliamentary group as he left the meeting on Tuesday evening.
"After the election declarations on Sunday, I said that there had been a change in circumstances," he said earlier.
"The attempt to find a negotiated Brexit between the Labour front bench and Theresa May had failed over the last few days, Theresa May has announced her resignation, and there is now a Tory leadership election and there have been in the European elections across the UK an upsurge in support for the Brexit Party, which is advocating a no-deal Brexit which I think would be disastrous economically.
"And so, the circumstances I think lead me to the conclusion, and I hope that this will become the adopted position of the Scottish Labour Party, that we will support, under all circumstances, a confirmatory referendum on any deal and that confirmatory referendum should also give people the option of voting to remain."
He also said the party had "failed" in its efforts to bring different groups of the electorate back together.
"The result on Sunday was extremely disappointing and we clearly failed in our bid to try to bring together a divided country, a division that exists between those who voted remain and leave in 2016, and frankly, a country that's also divided to some extent by the 2014 referendum here where people voted yes and people voted no.
"So we were genuinely attempting to bring those groups of the electorate together and it's clear from the results that came through at the counts on Sunday and into Monday that we failed to do that."
On Tuesday afternoon, the Labour group at Holyrood was locked in talks for around two hours.
A further meeting was scheduled for Tuesday after the resignation of Mr Johnson.
In his resignation letter on Tuesday, he said he had chosen to resign from the front bench due to the party's position on Europe.
Mr Leonard said: "Daniel Johnson was someone that I promoted into the shadow cabinet, he's somebody I've got an enormous amount of respect for, he's a talented person, and I'm sorry that he's decided to step down from the front bench but I'm sure that he'll continue to play an important role in putting forward the Scottish Labour case."
In his resignation letter, Mr Findlay said there was "eternal internal fighting" and a "toxic culture of leaks and briefings" by some MPs and MSPs in the party, although he insisted he had made the decision to resign in March.
Mr Leonard added: "There is debate inside the Labour Party and one of the things we've been discussing today at the Labour group is how we can improve working together because, in the end, no-one will vote for us if we are inward looking, we need to be outward looking and making the positive Scottish Labour case to the people of Scotland."