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.
"One of the points that I tried to make to President Putin is that Russia would be so much more attractive if it was aspiring to be a superpower for peace and freedom and prosperity ... instead of trying to recreate the lost glories of tsarism or the old Soviet Union."
Abbott, an athletic 56-year-old former amateur boxer whose government is a staunch U.S. ally, has gained a higher international profile by loudly demanding more cooperation from Russia on the Dutch-led investigation into the downing of Flight 17.
He raised eyebrows last month when he declared he intended to "shirtfront" Putin, using an Australian football term for a head-on shoulder charge to an opponent's chest.
Cameron also took a swipe at Russia, warning that Western sanctions against the country could increase if it continues to foster the rebellion in eastern Ukraine.
Meanwhile, German Chancellor Angela Merkel downplayed the appearance of Russia's ships.
"I find it much more serious that there are violations of Ukraine's territorial integrity," Merkel said during a press conference in Auckland, New Zealand, which she is visiting en route to the G-20.
Putin was expected to arrive in Australia for the summit in the eastern city of Brisbane on Friday.
Abbott has pushed to keep the G-20's agenda firmly focused on a plan to add $2 trillion to global GDP over five years, with countries expected to present reports on how they will achieve that goal this weekend.
World Bank President Jim Yong Kim on Friday praised the G-20, which is often criticized for being all talk and no action, for setting a clear target.
"We'll see what the results are, but we're already encouraged," Kim said. "If the countries will go through with the kinds of structural reforms that they've committed to, we could see a real bump in growth."
Australian Treasurer Joe Hockey has said the group will focus on infrastructure investment to help meet the goal. The World Bank estimates the financing infrastructure gap in developing economies is more than $1 trillion per year.
