Fires have razed more than 8 million hectares of land across Australia - an area nearly the size of Austria - killing 25 people and destroying or damaging thousands of homes.
Police on Monday confirmed the death of a 71-year-old man on the south coast of New South Wales state who was reported missing on December 31.
All missing people across the country have been accounted for, authorities said.
A second day of light rain and cool winds has brought some relief from heat-fuelled blazes that consumed parts of two states over the weekend, but officials warned the dangerous weather was expected to return this week.
Sydney did get some much-needed rain on Tuesday morning.
Insurers have received 8985 bushfire-related claims in NSW, Victoria, South Australia and Queensland since the Insurance Council of Australia declared a bushfire catastrophe on November 8 last year.
The Insurance Council of Australia increased its estimate for damages claims from the fires to more than $A700 million ($NZ727 million) on Tuesday, with claims expected to jump further when more fire-hit areas are accessible.
Thousands of people have been left homeless, while many in rural towns have spent days without electricity, telecommunications and, in some cases, drinking water. Military-coordinated rescue and support efforts were ongoing.
The New Zealand Defence Force said the first of three air force helicopters being sent to help departed on Monday, while the other two were expected by Wednesday.
Morrison, who has been criticised for his handling of the crisis, on Monday pledged $A2 billion to a newly created National Bushfire Recovery Agency - a commitment that could threaten his election promise to deliver the first budget surplus in more than a decade this financial year.
"There's going to be a very significant economic impact, but ... we want to get money out into these communities as fast as possible," Treasurer Josh Frydenberg told the Australian Broadcasting Corp ahead of planned meetings between Morrison and financial bosses.
"What we are focusing on here is the human cost and the rebuilding cost for people's lives," Morrison told reporters in Canberra. He said nearly 4000 cattle and sheep have been killed in the fires. Countless wild animals have been killed.
Victoria has set up a Bushfire Recovery Agency, with initial funding of $A50 million. The recovery is expected to cost "a lot more" than $A500 million, the state's Premier said.
On the ground, firefighters were working to get as much control over the huge blazes as possible before forecast high temperatures and winds return later in the week, threatening to ignite a fresh wave of fires.
"They are trying to secure fire lines where they can to try and minimise where these fires will burn again when conditions do warm up," Rob Rogers, NSW Rural Fire Service (RFS) Deputy Commissioner told reporters on Tuesday.
"We have no prospect of containment on all those fires, but we can use this time."
Almost 1600 homes have been destroyed in NSW, Australia's most populous state, authorities said. In Victoria state, authorities believe 300 homes have been destroyed.
Dean Linton, a resident of Jindabyne in the Snowy Mountains, used the break in the immediate threat to his town to visit his wife and four children who had fled to Sydney.
He also picked up a fire-fighting pump and generator to help him protect the family home.
"There's a lot of fuel in that national park; it would only take one lightning strike," Linton told Reuters.
The bushfire season started earlier than normal this year following a three-year drought that has left much of the country's bushland tinder-dry.
Meanwhile, Canberra was running short of masks as smoke blanketed the capital, ACT emergency services said.
The National Gallery of Australia said it was closed to protect visitors and art works. The government department responsible for coordinating disaster response also closed due to poor air quality.
