In a televised debate yesterday, leftist leader and former PM Alexis Tsipras said military action against people smugglers would not work in Greek waters.
"Operations of a military nature cannot be carried out in Greece's case, you will hit innocent refugees, not smugglers... The boats come without smugglers," Tsipras said.
His conservative rival Evangelos Meimarakis said that "illegal migrants" should be sent back to their country of origin.
Overwhelming Greece's Aegean Sea islands, migration has turned into a major issue ahead of the September 20 election, a campaign which had previously been dominated by the country's six-year economic crisis.
Tsipras and Meimarakis went into their second debate looking for an edge in the neck-and-neck race between their Syriza and New Democracy parties.
The debate was more lively than the first round on September 9 that also included another five parties.
He is asking for a second chance to put a human face on the unpopular 86-billion-euro (USD 97-billion) bailout he brokered with Greece's EU creditors in July.
"I could say the deal we brought is a living organism," he said, listing a number of "open issues" including debt reduction, privatisations, labour relations, and how to deal with non-performing bank loans.
"We will apply the deal, the section which we are obliged to apply, as fast as possible, and we will fight on major issues that remain open, for the benefit of the people," Tsipras said.
"The bailout includes reforms, restructuring, privatisations...We began them, we believe in them, we can do them," he said.
A Metron Analysis poll for TV station Antenna on Monday showed the two parties in a dead heat race, each attracting 24.6 per cent of the popular vote.