Pat Dodson said on Monday there was no point introducing constitutional recognition for Indigenous people unless those changes were made.
Politicians met with 40 Indigenous representatives in Sydney to discuss potential changes to the constitution.
Indigenous Australians are not mentioned in the Australia's founding document.
However, two so-called "race provisions" allow the states to disqualify people on the basis of their race from voting, and allow laws to be made based upon a person's race.
Mr Dodson - a highly respected Indigenous leader from Western Australia who has won the Sydney Peace Prize - said constitutional recognition for Indigenous Australians would not be worth pursuing if a non-discrimination clause wasn't added to the constitution.
"These are complex moral and ethical issues for some people but I don't think we should be discriminating against anyone in this nation, and certainly not against Aboriginal people," he told reporters.
Popular support
Prime Minister Tony Abbott has pledged to hold a referendum in 2017 that could see Aboriginal and Torres Strait Islander people recognised as the first Australians.
Opinion polls show there is widespread community support for the change.
However, there is still disagreement over the wording of any amendments.
Dozens of people protested outside Monday's meeting and said the participants did not have the authority to represent all Indigenous communities.
Symbolism
Mr Dodson said protections against discrimination needed to be strengthened.
"Two hundred years of discrimination is about as much as we can bear, quite frankly," he said.
Other leaders have expressed concern that any changes would be purely symbolic.
Mr Abbott and Opposition Leader Bill Shorten hosted Monday's meeting.
"Today was not a day to rule particular things in or out," Mr Abbott said later.
He said the next step would be to hold a series of community conferences later this year where the public could have their say on proposed changes to the constitution.
An Ipsos Fairfax poll released on Monday showed 85% of Australians were in favour of a clause being added to the constitution to recognise Australia's first people, up from 77% in 2013.
(BBC News)