The opposition leader said he thought "no meant no" when the prime minister initially declined his offer of more leaders' debates.
The Australian Greens immediately labelled the comment "inappropriate", prompting Mr Abbott to defend his choice of phrase.
"No means no" is usually used in the context of anti-rape campaigns.
On Monday, Ms Gillard offered to debate Mr Abbott on the economy after previously insisting there'd be just one head-to-head contest, which was held nine days ago.
The opposition leader said: "She's surely not trying to say to us that no doesn't mean no."
He later defended his choice of words on Brisbane radio.
"The Labour Party spin merchants are running around saying `This is terrible, this shows Abbott is insensitive to women," he said.
"I'm not going to cop this kind of vicious smear.
"I'm the father of three daughters - no one respects women more than I do."
Ms Gillard refused to buy into the barny, except to deny the ALP had attacked the Liberal leader.
"I don't see how Mr Abbott can say that," she told ABC Radio.
"I certainly haven't commented on the matter and I'm not intending to."
The prime minister wanted to focus on just one issue - the economy.
Ms Gillard used the Reserve Bank's decision to leave the cash rate unchanged to spruik Labour's economic credentials.
As was widely expected, the central bank left the cash rate at 4.5 per cent for a third straight month.
Ms Gillard said Labour made the better economic choices when the global financial crisis hit.
"On a day like this it brings into sharp relief the fact that economic management is at the centre of this election campaign," she said.
"If we'd done what Mr Abbott had advocated then we'd be in a recession now."
She said the election "at base ... is about our economy".
Mr Abbott begged to differ. For him - like Labor in 2007 - it's now all about working families.
"This election is not about Julia Gillard, it's not about the Labour Party, it's actually about a better deal for the struggling families of this country," he said when relaunching his $8.8 billion parental leave scheme.
It will now start in mid-2012, a year later than expected, and be funded by a 1.5 per cent levy on big business, down from a 1.7 per cent.
The opposition leader said his scheme would be good for the economy because it would boost population, participation and productivity.
Families Minister Jenny Macklin borrowed a favourite line of Mr Abbott's to attack the coalition's scheme.
"Mr Abbott wants to introduce a big new tax - 1.5 per cent tax - on everything you buy every time you go to the supermarket," she told reporters in Sydney.
"Every single business that has this new tax imposed on them will pass it onto consumers."
Ms Gillard was also happy to borrow from Mr Abbott.
After he said on Monday he was facing "the supreme challenge of my life", she declared on Tuesday: "This is the fight of my life ... so I'm not going to die wondering."
