In recent days, four Russian warships have entered international waters off the northeast Australian coast to coincide with Putin's visit to Australia for the summit that brings together the leaders of the world's 20 biggest industrialized and developing economies. Australia, in turn, sent three warships of its own to monitor them.
The Russian embassy said on Friday that Russia's Pacific fleet was testing its range, and could be used as security for Putin.
Abbott was not impressed.
"Russia is being much more assertive now than it has been for a very long time," he said at a press conference with British Prime Minister David Cameron, also in Australia for the summit. "Interestingly, Russia's economy is declining even as Russia's assertiveness is increasing."
The prime minister, who met with Putin earlier this week on the sidelines of the Asia-Pacific Economic Cooperation forum in Beijing, aired details of his conversation with the Russian leader.