Howard, whose eight-year-old government trails in opinion polls, has accused Latham of misleading the parliament over intelligence briefings which formed part of Labour's pledge to bring Australia's troops home from Iraq by Christmas.
Australian troops participated in combat operations during the war on Iraq.
In the parliament
Howard attacked his rival, 21 years his junior, as an inexperienced politician, flushed by favourable opinion polls and making policy on the run.
But Latham countered this in parliament on Wednesday by saying Labour had decided a year ago, as part of its anti-Iraq war policy, that Australian troops should be brought home.
Latham branded President Bush
as 'incompetent and dangerous'
"The leader of the opposition has been in the business of misinforming the Australian public," Howard told parliament.
Latham charged Howard with being reckless in committing troops to the US-led war with no exit strategy, accusing him of plotting to bring troops home during the election campaign.
"It is always sad to see a politician at the end of his long career, the twilight months, thrashing around for an issue," Latham told parliament to cheers from his Labour
Latham's decision last week to bring 850 troops home for Christmas should he win the election saw him take the initiative on security, prompting Howard to reveal details of top-secret briefings between Latham and intelligence agencies to try to damage his credibility.
Latham told parliament on Tuesday that he had "lengthy discussions about Iraq" with intelligence officers which formed part of his decision to bring troops home.
Howard, however, produced a letter from the head of the Australian Secret Intelligence Services (ASIS), whose agents spy overseas, that stated he did not discuss Iraq at a meeting with Latham.
"It is always sad to see a politician at the end of his long career, the twilight months, thrashing around for an issue"
Australian Labour party Leader
But Latham was adamant that he was well briefed on Iraq by ASIS and a senior defence official.
"This is the truth and I again ask the prime minister to apologise and withdraw," Latham said in a personal explanation delivered in parliament on Wednesday.
The fate of Australia's troops in Iraq has put Howard and Latham at loggerheads, making it a likely election issue, with an AC Nielsen poll on Tuesday showing 61% of Australians want troops to stay in Iraq until post-war reconstruction is complete.
Howard argues that withdrawing troops would be seen as bowing to terror groups after this month's attacks on commuter trains in Madrid. Latham argues Australia's domestic security should take priority to overseas security commitments.
But while security dominates the political debate, Australia's booming economy, with interest rates near 30-year lows and unemployment at 14-year lows, is more than likely to eventually take centre stage at the ballot box.
Howard has plenty of time to reverse his fortunes and the economy remains one of his most potent weapons.