Speaking on the Gallipoli Peninsula on Thursday before the 100th anniversary commemoration of the Battle of Lone Pine, Mr Cosgrove said Australians "should feel for Turkey", which is caring for about two million refugees displaced by the conflict in Syria.
"That conflict meant Turkey had a problem with security and a very unstable border," he said. "While in that respect it is profoundly a problem for the Turks, we must do whatever we can to support peaceful outcomes.
"Peaceful outcomes obviously means there are no more atrocities happening across Turkey's borders," Mr Cosgrove told reporters, referring to terror acts being carried out by the Islamic State group in Syria.
He said cooperative arrangements made between the Turkish and Australian governments about the issue of terrorist access through Turkey were very important to the Turks.
When asked whether Turkey's decision to allow US drones and jets to use two of its airbases to launch raids against IS targets in Syria would affect the deployment of Australian aircraft also tasked with attacking IS, Mr Cosgrove said the Australian commitment was to Iraq.
"We have a relationship with Iraq, an Iraq that struggles now and I think it's quite proper that we are supporting Iraq in their particular problem."
Mr Cosgrove is attending the Lone Pine commemoration with the parents of Victoria Cross winner Cameron Baird, who was killed in action in Afghanistan in 2013.
Also attending are VC winners Mark Donaldson, Daniel Keighran and Keith Payne to mark a battle in which about 800 Australians were killed and about 1500 wounded in fierce fighting over Turkish trenches.
The governor-general said Gallipoli was a touchstone in the relationship between Turkey and Australia and that relationship had endured and strengthened over the years.
Earlier on Thursday, Mr Cosgrove laid a wreath at the memorial to Turkey's 57th Regiment, which was wiped out in the fighting at Gallipoli.
"On the first day of the landings the 57th Regiment played a crucial role in stopping the Australian and allied advance to the high ground. This regiment spent itself for Turkey," he told reporters.
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