Burton rules out any Labour link with Sinn Fein/IRA in coalition
Ms Burton, speaking during the first Labour leadership debate, said Gerry Adams' party was a long way from "true democracy" and still had questions to answer over its links to the atrocities of the Troubles.
She was applauded by party members when she condemned Sinn Fein for its links to the Provisional IRA and the death of Jean McConville.
She categorically ruled out the Labour Party under her stewardship "making up the numbers" with Sinn Fein in a future government.
However, Junior Health Minister Alex White, who is also running for the leadership, said he "abhors" Sinn Fein's policies but would not rule out a coalition with the party as an "article of faith".
Both leadership candidates were grilled by party members during a debate dominated by discussion on Sinn Fein.
Mr White said he would retain Ms Burton as a minister should he be elected as leader of the party.
But in a blatant snub to her rival, Ms Burton refused to say if she would keep Mr White as a minister should she win vote. Instead, the minister said she would appoint the "best people" to Government.
Earlier, Mr White ruled out slashing €2bn from the Government's balance sheet at the next Budget. He proposed missing the EU imposed deadline for bringing the Government's deficit below 3pc next year, saying people have "reached the end of the line" when it came to cuts and tax increases.
"There can be no question of an adjustment of the order of €2bn next year," he added.
"We have an agreed target of reducing the deficit below 3pc in 2015 but if we were to miss that deadline marginally or by a few months so be it I say."
His stance would likely lead to Coalition tensions ahead of the forthcoming Budget.
Ms Burton said she would clamp down on tax shelters and hike taxes for millionaires if she was elected.
"I want to phase out any remaining tax shelters that favour the very wealthy, so that we can concentrate tax relief on where it's needed most – for low and middle-income families," he said.
Mr White and Ms Burton were speaking at the first of the five Labour leadership hustings, held at the Radisson Hotel beside Dublin Airport.
Another round of debates are scheduled for next week in the Communications Workers' Union (CWU) headquarters on Dublin's North Circular Road.
Debates will also take place in Galway, Cork and Portlaoise.