The iwi disputes the settlement agreement that Little has indicated he is willing to sign with Pare Hauraki, a collective of 12 Hauraki iwi.
Charlie Tawhaio, chairman of the Ngāi Te Rangi Settlement Trust, said it welcomed the extension, "as brief as it is".
"We are committed to engaging with the respective iwi of Hauraki in a tikanga process. We hope that we can make sufficient progress in the next week to satisfy the minister that we are sincere in our efforts to engage."
The extension will also give Minister for Māori Development Nanaia Mahuta - also the MP for Hauraki-Waikato - more time to organise a meeting between the two parties.
Mahuta told the hīkoi she was willing to try to arrange a hui on neutral ground if there was enough goodwill on both sides to make it useful.
"Let's have that hui," she said, to cheers and clapping from the protestors.
"Maybe that's what I can do as a local MP with a belief that there is a will to move forward."
Little said Mahuta's offer was a "good positive step" that could bring about a result.