"This will inevitably have a significant, but limited, impact on services, programs and support functions and on staff and volunteers in specific areas," wrote Mr Tickner, who was a minister for indigenous affairs in the Hawke and Keating Labor governments.

A spokesman for Mr Dutton said the government was "extremely grateful" for the work performed by the Red Cross, but it was "not strongly related to the health portfolio".

"For that reason we have redirected funding into other worthy causes more closely related to the portfolio," the spokesman said.

"The Australian government, through various other departments, has provided a significant amount of funding to the Red Cross Society in annual grants."

Labor's health spokeswoman, Catherine King, said: "It says a lot about this government's priorities that Tony Abbott can find $1 million to buy a mansion in Melbourne for the Australian Ballet at the same time as cutting $5 million from the Red Cross, an organisation that supports some of the most vulnerable Australians when they are in need."