Malcolm Turnbull says he has no intention of giving Germany gratuitous advice about how to handle the flow of asylum seekers from the Syrian conflict.
The deadly attacks in Paris have sparked a debate in Germany on Chancellor Angela Merkel's refugee policy and how to get a better overview of the people entering the country.
German officers indicated that Merkel noticed no purpose to revise her stance on refugees in the wake of the Paris assaults.
"Each country faces very different circumstances, not the least of which are geographical".
"The chancellor has the situation under control..."
Germany expects a record 800,000 migrants at its borders for the whole of 2015 - four times the number of asylum applications received in 2014 and nearly double the all-time high of 438,000 in 1992. Politicians from around the world have condemned the attacks.
The pair also discussed military vehicles. "The solution will ultimately be a political one".
Mr. Turnbull arrived in Berlin late yesterday after flying from Jakarta, where he held his first meeting with Indonesian President Joko Widodo during a visit that established a cordial relationship between the two leaders.
There are reports the US president, Barack Obama, may meet the Russian president, Vladimir Putin, over the coming days at the G20 summit, with Syria expected to be a major focus of the talks in Antalya.
But Germany's top security official also has warned that two-thirds of suspects linked to attacks on refugees and asylum homes were previously unknown to the police.
The recommendations suggest closer ties across the spectrum, ranging from trade and investment, science, national and strategic security, the arts, education, culture, energy and politics.
Mr. Turnbull said he was "overwhelmed" seeking economic outcomes from the summit, building on the work of the 2014 Brisbane summit.
Germany and Australia on Thursday signed a treaty to deal with "double taxation", which came out of the study, and Australia will appoint a trade commissioner in Frankfurt.
Asked during the press conference for her views about Mr Abbott's recent speech in London, in which he warned Europe's "misguided altruism" towards those fleeing Syria would have catastrophic consequences, Dr Merkel was diplomatic. Japan has said it is ready to match its European rivals and build a fleet of submarines for Canberra entirely at Australian shipyards.