Christians Against Poverty is making the appeal on the 13th annual World Suicide Prevention Day.
Figures from the Office for National Statistics show that there were 6,233 suicides in Britain in 2013 - 252 higher than the previous year.
Laura Roberts, New Enquiries Team Manager at CAP, said: "We are really passionate to see more churches work with us to prevent more people feeling this way and getting to that point [committing suicide] in particular."
"World Suicide Prevention Day really strikes us at CAP because 34% of the clients that have come to us for debt help said that they felt suicidal. So the poverty that they were suffering from really did have an impact, to the point where they were either considering or had even attempted suicide."
Ms Roberts added that the number of people taking their own lives in Britain is "shocking" and that to see an increase is "horrendous".
"We really want to empower the church and say 'You can be a part of tackling that'".
World Suicide Prevention Day is jointly hosted by The International Association for Suicide Prevention, The World Health Organization and the World Federation for Mental Health.
Prof. Ella Arensman, President of the International Association for Suicide Prevention (IASP), said: "Suicide represents a serious global public health problem. Every year more than 800,000 people die by suicide. This corresponds to one death every 40 seconds."
"When a suicide occurs this has a major and long-lasting impact on family, friends and community members who are left behind. Often people experience very intense and recurrent emotions such as guilt, self-blame and anger and they may not feel that they can share this overwhelming feeling and impact with others."
Prof. Arensman believes the stigma still attached to suicide and mental health problems prevents those contemplating suicide and the bereaved from seeking help.
The reasons why people choose to take their own lives are difficult to measure but for Christians Against Poverty debt is a problem that they often see leading to suicide.
Laura Roberts said: "A lot of people say to us that they just do not see a way out. They have got people hammering at the door, they have got phone calls and they have got letters coming through the door. It is really quite scary for them and those thoughts do creep in: 'Have I got any other way out?'
"There is a way out. We are a free service. There's no judgement whatsoever. We want you to see what we can do to move forward and look at plans to deal with the debts or to help you back into work. There are solutions out there."
To help get the message across CAP is asking for more churches to partner with them.
"CAP can train you, we can support you to go to your community and put you in touch with those people who are in need."