Several hundred protesters have marched on Jacinda Ardern’s Auckland office, demanding she visit Ihumātao, the site of a major indigenous land dispute that has broadened into wider anger at government inaction in tackling Māori disadvantage.

The protesters delivered a petition, signed by more than 26,000 people, to the prime minister’s office urging her to travel to the site that has been occupied for the past month as part of a housing dispute.

“We battled high winds, we battled pouring rains and we are still here,” said one marcher of the 18km journey. The protesters then finished the hikoi [protest march] with a prayer and a song before dispersing.

The Ihumātao protest is an occupation of the land near New Zealand’s earliest market gardens. It is considered a sacred area, as well as being a significant archaeological site. However, Fletcher Building is planning a housing project, which hopes to develop hundreds of homes in the area.

Last month, Ardern asked Fletcher Building to halt any further development until the stand-off was resolved but she has been criticised for failing to visit the peaceful occupation, and her Labour coalition government has drawn increasing ire for failing to improve the lives of the country’s indigenous people – despite having the most Māori MPs of any political party in New Zealand’s history.

“We are walking to invite Jacinda Ardern to our whenua [land], so she can experience the same feelings we experience every day,” protest leader Pania Newton said before the protest march. “She has a responsibility to come here.”

Ardern was not at her electoral office to greet the hikoi, but said: “But if they wish to know they’ve been heard, I can tell them now, I’ve heard them, I know the issues and that’s why we’ve been involved in trying to help find a solution.”

She has not ruled out visiting Ihumātao in the future but said talks about the issue were underway. “I want to respect that process. That’s the place where we’re going to get a solution.” Ardern also said she was open to speaking to protest leader Pania Newton.

Last month the Māori king, Kiingi Tūheitia, offered to act as a facilitator to negotiate the stalemate between Ihumātao’s iwi authority, which supports the building development, and those who are against it, led by Newton and the Save Our Unique Landscape (Soul) group.

People left fruit and water along the route of the march as they walked through heavy rain along a path next to the state highway. Others were asked to join in as they made their way to Ardern’s office. The petition grew by several thousand signatures during the hikoi.

Local police superintendent Jill Rogers said police recognised everyone’s right to freedom of peaceful assembly. “Police will be monitoring the event to ensure the safety of everyone involved and to ensure there is minimal disruption for the general public as a result of the hikoi,” she said.

The protest movement has even reached the streets of London with artists have showing support for Ihumātao. Protest Stencil placed handmade posters around London Transport bus stops and other advertising spaces on Monday.