The meeting with Najib Razak comes ahead of an intensified search for Flight 370, which is believed to have crashed in the southern Indian Ocean six months ago.
They will also discuss MH17, which exploded over strife-torn eastern Ukraine in July, Malaysia's Foreign Ministry said in a statement.
The West has blamed Russian-backed separatists for shooting down MH17, while Moscow blames Kiev.
Mr Abbott's one-day visit is his first since becoming prime minister in September last year.
"High on the agenda is discussions on the status of the two countries' cooperation in relation to Malaysia Airlines Flight MH370 and Flight MH17 incidents," the ministry said.
The two premiers will meet with Malaysian personnel involved in the missions to find MH370 and to salvage wreckage and remains from the MH17 crash site.
They will also discuss other "regional and international issues of common concern".
"This visit will undoubtedly further cement the close and outstanding relations between the two countries," the ministry said.
Later in the day, Mr Abbott will meet business leaders as well as educationists to present his government's New Colombo Plan, a scholarship program to encourage more Australians to study across the Indo-Pacific region, officials said.
Australia is leading what has so far been a fruitless search in a vast stretch of the southern Indian Ocean, where MH370 is believed to have gone down after inexplicably veering off course from its Kuala Lumpur-Beijing route on March 8.
The Boeing 777-200 was carrying 239 people.
Australian authorities said on Friday that "hard spots" had been found on the Indian Ocean seabed but they would most likely be geological features.
Experts are preparing for a more intense underwater search to begin this month in a dauntingly vast stretch of ocean measuring 60,000 square kilometres, in addition to ongoing mapping through a sonar survey.
Malaysia's government and the national flag carrier were widely criticised over what many saw as a disorganised and secretive response to MH370's disappearance.
Flight MH17 went down in Ukraine on July 17, killing all 289 people aboard, including 38 Australian citizens or residents.
Dutch air crash investigators have announced they will release a preliminary report on Tuesday into what brought down the flight, travelling from Amsterdam to Kuala Lumpur.
The Netherlands is leading the probe into the crash, which killed 193 Dutch citizens.
It follows Mr Abbott's two-day visit to India, which saw the signing of a landmark agreement allowing Australia to sell uranium to the country.
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