Prime Minister Tony Abbott said boat arrivals were down 90 percent from the peak of arrivals under Labor, The Age newspaper reported.
"I can say to you with great confidence, my friends, they are stopping. They are stopping and they will be stopped," Abbott said.
But Abbott's comments prompted Labor's immigration spokesman Richard Marles and former immigration minister Tony Burke to claim Abbott is reaping the rewards of Labor's efforts before the party lost the election in early September.
Marles told Fairfax Media former Prime Minister Kevin Rudd's decision in July to send asylum seekers to Papua New Guinea and the Micronesian island nation of Nauru, coupled with Labor's pledge not to resettle any boat arrivals in Australia, have been a "game changer."
Marles said by August there had been a 40 percent drop in arrivals.
The war of words is a continuation of Australia's ongoing struggle with the emotive issue of how to accommodate thousands of asylum seekers arriving in territorial waters in rickety vessels.
Liberal and Labor parties have been fighting over how to treat the asylum seekers fairly and with compassion, but put an end to the human trafficking by ruthless people smugglers in Asia.
Abbott's Liberal government's Operation Sovereign Borders plan includes a senior military commander as head of a force to go after people smugglers and to coordinate boat arrival operations.
Australia's 12 agencies involved in border protection are re-organizing under the command of a single three-star military commander.
An investigative report in the Sydney Morning Herald earlier this month found 1,500 asylum seekers have died trying to reach Australia since 1989.
The worst disaster was in October 2001 when the SIEV X sank, drowning 146 children, 142 women and 65 men, the Herald reported.
The death toll reached 1,500 last month when a boat sank off Indonesia's Javanese coastline with the loss of as many as 50 people, including two children.
The Herald report is based on a Fairfax Media investigation of more than 1,100 boats and nearly 70,000 people who have set out since 1989 -- 40 of the journeys have resulted in drownings.
The investigation of boat arrivals -- mostly from Indonesia -- compares the rate of boat journeys per 100 days and drownings per 1,000 passengers under each prime minister in the period.
The number of boat arrivals under Julia Gillard's Labor prime ministership from 2010 to June this year was 55 per 100 days, with the mortality rate of 22 per 1,000 asylum seekers.
Prime Minister Kevin Rudd's three-month premiership -- he unseated Gillard in a bitter internal Labor party leadership contest -- was a peak rate of one boat every day during the 100 days. However, the death rate was lower, at 7 people per 1,000 passengers.
So far Abbott's government has had 8 incidents, making the ratio the equivalent of 57 boats per 100 days, the report estimated. During this time, 56 asylum seekers drowned, the equivalent of 155 per 1,000 passengers.
Rudd's policy, still followed by Abbott, of sending asylum seekers to detention camps in Papua New Guinea and Nauru, is mired in controversy.
The West Australian newspaper reported this week asylum seekers detained in Papua's Manus Island detention center accused Australian officials of abandoning them when a violent brawl erupted between rival Papuan security forces.
Royal PNG Constabulary officers clashed with PNG Defense personnel on the outside perimeter of the detention center on Oct. 18.
The West Australian reported armed PNG police were pushed and shoved by members of the PNG Defense Force carrying rocks and sticks.
Detention center personnel, including from Australia's Immigration Department, the Salvation Army, security firm G4S and contractor International Health & Medical Services, were moved into a secure area of the compound in case an evacuation was ordered to a waiting Australian naval ship.
Many of the 1,060 asylum seekers at the center used social media to criticize Australian officials for leaving them in a potentially dangerous situation, the West Australian report said.