France's National Assembly has supported the return of up to 20 Maori heads to New Zealand and is due to vote next week to give them back.
Between 15 and 20 mummified heads of Maori are stored in several French museums.
A museum in Rouen offered to return its Maori heads to New Zealand in 2007, but the French government stepped in and put the decision on hold.
Now all the political parties in France have said they would back a bill ordering the return of certain artefacts.
New Zealand's Ministry for Culture and Heritage says Te Papa is the Crown's agent for repatriation of the skeletal remains, known as koiwi tangata. Once the bill is passed, it says, Te Papa will work with iwi to determine the final resting place of koiwi tangata.
Museums around the world have held up to 500 Maori heads, but about 300 have been returned at New Zealand's request.
