A joint statement signed by 10 leaders also implores the public to treat those standing as candidates with respect.
It comes after the Catholic Bishops' Conference of Scotland issued a pastoral letter to be read out at services, calling on members of the congregation to elect MPs who "reflect as close as possible their beliefs".
The statement said: "As the UK General Election approaches on 12th December, we would like to remind people of the hope that we share as we approach this special time of year - of new life and a new world, and the inspiration this gives us to create a better society for us all - one in which we truly care about those around us.
"We would urge people to treat those who are standing for public office with respect and to use a tone in our debates that recognises the human value in all of us - even, and especially when, we disagree.
"We are all entitled to our own opinions and strong beliefs, and debates sometimes do get passionate and vigorous. But let us ensure that truthfulness and integrity are at the forefront of what we say and do."
The statement also said the creation of a more equal society is something people can all agree on.
It said: "As people of faith, we believe in the flourishing of local communities and the importance of acting to make sure this can become a reality.
"There are many issues which divide us but many more that can unite us - and the realisation of a fairer, more equal and more just society is one of them."
The statement was signed by the Rt Rev Colin Sinclair, moderator of the General Assembly of the Church of Scotland, Hugh Gilbert, Bishop of Aberdeen and President of the Bishops' Conference of Scotland, and Most Rev Mark Strange, t Primus of the Scottish Episcopal Church.
United Free Church of Scotland moderator Rev John Fulton, Methodist Church in Scotland chairman Rev Mark Slaney, Scottish Unitarian Association president Joan M.M. Cook, Quaker leader Adwoa Bittle and the Rev Dr David Picker, moderator of the United Reformed Church National Synod of Scotland, also put their weight behind the statement.
The list is completed by Lieutenant Colonel Carol Bailey, Secretary for Scotland at the Salvation Army, and Congregational Federation in Scotland chairwoman Rev May-Kane Logan.
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