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Life Matters Suicide Prevention Trust chairwoman Corinda Taylor set up the petition last week before Mental Health Awareness Week this week.
She hoped the response would prompt the health select committee to follow up the trust's push for a mental health inquiry.
A petition organised ahead of the trust's May health select committee appearance garnered just 1740 signatures, Mrs Taylor said.
''We hope that this online petition, once we have even more ... signatures, can be tabled with our original petition once the new government is formed.
''I did this new online petition in frustration because the health select committee [is] not communicating with us or including people with the lived experience in this consultation process.
''I also want to acknowledge the people in our trust, Denise Kent and Carolyn McMillan, for their endless support and energy for helping, supporting and making sure we stay true to our values that good mental health support is a basic human right,'' Mrs Taylor said.
She said she was touched by the comments people lodged with their signature expressing support.
Events are being held throughout Otago and Southland for Mental Health Awareness Week, the theme of which is connecting with nature.
Yesterday, Otago Polytechnic held a ''lockout'', encouraging people to spend time outside playing games, eating fruit and listening to music.
The Mental Health Foundation has encouraged workplaces to take part in ''lockout'' events during the week.
Other events in the region include community bike rides, walks, and barbecues.
WellSouth health promotion specialist Jo O'Connor said there were many ways people could be with nature and improve their wellbeing.
''For some people, connecting with nature means taking time to look out the window or keeping a photo of a special place on your desk.
''There are lots of meaningful ways each of us can unlock our wellbeing by spending time with nature every day.''
Healthline: 0800 611-116
Lifeline Aotearoa: 0800 543-354
Suicide Crisis Helpline: 0508 828-865
Samaritans: 0800 726-666
Alcohol Drug Helpline: 0800 787-797
General mental health inquiries: 0800 443-366
Depression Helpline: 0800 111-757
Youthline: 0800 376-633, txt 234 or firstname.lastname@example.org