Harry, patron of the games for injured and sick service personnel, was in Sydney to promote the sporting extravaganza he said proved it was possible to overcome adversity.
"I would like to start by sending my thoughts to those affected by Saturday's attack in London Bridge," the former soldier said as rain pounded down outside Admiralty House, home of the Queen's representative in Australia Peter Cosgrove.
"And our hearts go out to the victims, their friends and families."
Two Australians were among seven people killed in Saturday's attack when three men, wearing fake suicide vests, mowed down pedestrians on London Bridge in a van before slashing and stabbing revellers in Borough Market.
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It followed the May 22 suicide bombing at the Manchester Arena, killing 22 people, including children.
"When a bomb left a number of people with life-changing injuries in Manchester last month, wounded veterans, including Invictus team members, immediately offered advice and support to the victims through the recovery process," said the prince.
The next Invictus Games -- which launched in 2014 -- is in Toronto this year, before moving to Sydney in 2018.
Harry said sport could bring people together and for those recovering from injury, the Games gave them a sense of purpose.
"The Invictus Games show us it is possible to overcome adversity and that the impossible is possible if you have the will," he added.