Polls suggests neither are likely to secure a parliamentary majority.
Mr Tsipras called the snap election after securing a multi-billion euro bailout last month.
Vangelis Meimarakis - voice of reason or throwback?
In the debate, hosted by state broadcaster ERT, Mr Meimarakis said Greeks wanted the stability that only a grand coalition could bring.
"We can have a national team not only in the governance of the country, but also a national negotiating team [for Greece`s bailout]," he said.
But Mr Tsipras replied that the two had "fundamental differences" and so a unity government would not be possible.
"Tsipras wins out but the opponent was dead! In fact, Tsipras did not win, Meimarakis lost!"
The debate was billed as a chance to win over crucial undecided voters, with both parties drawing 31.6% in a recent poll for ANT1 TV.
A first debate included five other parties, but this one allowed the two men to ask each other questions and comment on answers.
Mr Tsipras won power earlier this year pledging to end austerity, but was instead forced to accept a rescue package that included more cuts.
He has said he wants to continue to fight against poverty and corruption, while Mr Meimarakis has accused him of wrecking the economy while in power.
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