Coleman made his comments at Parliament as the Herald highlights the issue of youth suicide in a special series called Break the Silence.
New Zealand ranks second worst in the developed world for suicide in those aged 25 and under. It is the worst in the world for suicide in those aged 15 to 19. The suicide rates have remained largely unchanged for two decades.
• Break The Silence: Q&A on Herald special series
• Investigation: The untold story of teen suicide in the North
Asked what could be behind those statistics, the Health Minister said the situation was complex.
"There are a range of pressures, certainly society with pressures of social media on young people, it is an issue that all societies, all Western countries are grappling with. And we've all got to do better on it."
On whether schools should hold suicide awareness days, Coleman said suicide needed to be discussed, but in the appropriate context and with adequate support in place.
Prime Minister Bill English said talking about suicide was a "difficult balance".
"Anyone who has experienced it knows that it can have quite a destabilising effect for young people. It can be glamorised. In that context a discussion is dangerous.
"On the other hand, sometimes if they are aware of what is going on, particularly with their own peers, then they can be effective in preventing it. It is a pretty difficult balance."
Opposition parties have targeted the Government's record on mental health, with Labour leader Andrew Little saying his party will make improving the system a priority if in Government.
As part of Budget 2017, an extra $224m will be invested into mental health services over four years. About $25m a year will go on new "innovative" proposals to tackle mental health issues.
Officials are currently looking at the possible link between the use of digital technologies and surging demand for mental health services.
Director and Chief Advisor of Mental Health Dr John Crawshaw told the Herald last month the link could be particularly strong for children and teenagers.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• LIFELINE: 0800 543 354 (available 24/7)
• SUICIDE CRISIS HELPLINE: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757