It will be replaced with a revamped families package.
"There will be an emphasis on child care and how we can build and boost female workforce participation," Mr Frydenberg said.
It was too difficult to proceed with Mr Abbott's "signature" parental leave policy given the tight budgetary environment.
"The prime minister recognises that he has to be pragmatic about it," the assistant treasurer said.
He batted away criticism of the decision, saying Mr Abbott had consulted colleagues extensively and taken into account the Productivity Commission's report into child care.
"You can't criticise him for taking leadership on this issue even though he said at the last election that we're going to introduce the PPL."
Queensland MP Ewen Jones said he knew many women who would be deeply disappointed by the decision.
"But it was too hard a sell, and it has to go," he said.
Abbott under fire
Deputy Prime Minister Warren Truss says he has no doubt Tony Abbott has the support of his colleagues and is working hard to listen to public concerns.
The prime minister's leadership is under mounting pressure as he prepares to deliver today's policy speech.
Mr Truss is among a number of senior government figures rallying to Mr Abbott's support after the Queensland election, poor recent opinion polls and his widely-criticised move to confer a knighthood on Prince Philip.
"I've got no doubt that Tony Abbott enjoys the support of his colleagues," Mr Truss told ABC radio on Monday.
In a bid to show he's listening to his backbench, Mr Abbott is reportedly instituting a number of internal changes to improve consultation with colleagues.
Cabinet will meet once a month instead of quarterly, while a new backbench policy advisory group will be established, the ABC reports.
Asked whether colleagues privately held different views about Mr Abbott's leadership, Mr Truss suggested his "patriotic" response was to work hard to earn the respect of the Australian people.
"There will have to be changes of direction and we'll have to work very hard to take the people of Australia with us," he said.
Queensland MP Ewen Jones says Mr Abbott will have to demonstrate he cares and is listening.
"That he gets what he's on about; that he's putting the government on the front foot, that we don't make mistakes, we don't make stupid errors," he told the ABC.
Independent Senator Jacqui Lambie said Mr Abbott should accept blame for the LNP's disastrous results in the Queensland election.
"As soon as Tony Abbott admits that, the sooner we can move on and the sooner someone can take over his leadership."
Foreign Minister Julie Bishop joined Mr Truss in backing the prime minister.
"Tony Abbott does have my support," she told reporters in Sydney.
Assistant Treasurer Josh Frydenberg said Mr Abbott had the experience and personnel to claw his way back in the polls.
"He's not finished," he told ABC radio.
"Yes, our backs are against the wall but yes, we can get back from here."
The coalition would not resort to ALP tactics, he said.
"We're a lot better than the Labor party, we don't treat leaders like a game of pass the parcel.
"The Liberal party has never tossed its own prime minister in its first term ever since its foundation and I don't think we should start today."
- AAP
