Mr Abbott opened the new headquarters of the South Australian Health and Medical Research Institute (SAHMRI) on Friday, which was financed partly by a $200 million grant from the previous Labor government.
He acknowledged the provision of the funds by former Prime Minister Julia Gillard but said considering the work that would be done in the new centre, it was not something that belonged to one side of politics or the other.
"In the end it doesn't even belong to Adelaide or to South Australia," Mr Abbott said.
"It belongs to humanity because all of humanity will benefit from the work that is done in this building."
South Australian Premier Jay Weatherill said the new building was symbol of the state's growing ambitions.
"With state-of-the-art laboratories and equipment, scientists and clinicians will work together in search of better treatments and cures for some of our most challenging diseases," he said.
The new facility will focus on a seven areas of research - cancer, nutrition, infection and immunity, heart health, mind and brain, health mothers and babies and indigenous health.
It is the first part of a new health and medical precinct in Adelaide which will be the biggest in the southern hemisphere once other research teaching facilities are completed along with the new Royal Adelaide Hospital.
SAHMRI executive director Steve Wesselingh said the new facility would be a clear focus for medical research in Australia.
"It will allow us to do some of the best medical research in the world and improve the delivery of health care across the world," Professor Wesselingh said.