The Northern Territory senator was sworn into the ministry by Governor-General David Hurley at Government House on Thursday.

Senator McCarthy was unable to participate in the first ceremony held at the beginning of June, after testing positive to COVID-19.

"It's a real honour, I'm very excited ... to not only serve the NT as a senator, but to also serve in an Albanese Labor government," she said.

Senator McCarthy said commitments taken to the election campaign focused on health policies, but also included improving access to education and job opportunities for people in regional and remote communities.

A key focus would be closing the gap in life expectancy between Indigenous and non-Indigenous people, with better health outcomes being essential to improving the lives of First Nations people.

Senator McCarthy said she will be working closely with Indigenous Australians Minister Linda Burney - who was appointed to cabinet - on progressing a constitutionally enshrined voice to parliament in the government's first term.

The Albanese government has pledged to hold a referendum on enshrining the voice in the constitution.

A "voice" would be a body made up of First Nations people that the government would need to consult with on policy, so they can have their views heard on the laws that will impact their communities.

The government has previously said the referendum won't be called until it is confident it will succeed, which will require bipartisan support.

Opposition Leader Peter Dutton has said he is open to the voice, but wants to see the detail before making a commitment.

Foreign Minister Penny Wong in a joint press conference with her New Zealand counterpart on Thursday, said Australia should "integrate" First Nations culture "into how we engage with the world and how we talk to and with the world and about ourselves".

Senator McCarthy said it was "fantastic" the government was throwing its support behind drawing on First Nations' historical relationships with neighbouring nations.

The Australian Electoral Commission on Tuesday formally declared Senator McCarthy had been elected to the Senate for the NT, alongside Country Liberals senator Jacinta Price.

Australian Associated Press