The People Before Profit leader said there is an historic opportunity to “break the cycle of Fianna Fail and Fine Gael” and elect a left government.
Richard Boyd Barrett said there was a “desperate desire” to remove two of the biggest parties from power.
Referring to recent opinion polls, he said that around 60% of people have indicated they want an alternative to Fianna Fail and Fine Gael.
He urged the public to “vote left and transfer left”, adding that 100 years of the two big parties should end.
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He also criticised left parties who might “prop up” Fianna Fail and Fine Gael.
Speaking in Dublin on Wednesday, he said: “There is a desperate desire to remove Fianna Fail and Fine Gael, and there is an historic opportunity to do so.
“Sixty per cent of people – that’s what the polls are telling us – want an alternative to Fianna Fail and Fine Gael, and this creates an historic opportunity for a left government, as People Before Profit has been saying from the outset.
“We have to grasp this opportunity to move away from Fianna Fail-Fine Gael government.
“If we are going to move away from decades of Fianna Fail and Fine Gael government that have only represented the very wealthy, big businesses, the landlords, the banks, and represent the working people, young people and the vulnerable in our society, we need to vote left.
“Vote for People Before Profit but also transfer left and we urge the other parties to transfer left and recognise this opportunity and to finally rule out another round of propping up the cycle of Fianna Fail and Fine Gael.
“Ordinary people are telling us they want an alternative to Fianna Fail and Fine Gael. There is a fantastic response to People Before Profit that they can have a government that doesn’t represent a minority of very wealthy people, of big profit and big business.
“We are not propping up Fianna Fail and Fine Gael, we want to see a government of the left, and we urge other parties on the left to grasp this opportunity also by ruling out another round of Fianna Fail and Fine Gael and show people a genuine alternative.
“The people who need the change the most often don’t vote as they think they will get the same old politics.”