The Church of Scotland and the Humanist Society of Scotland have called for legislation to be introduced to change the name of "Religious Observance" to "Time for Reflection".
They say it would make the events more inclusive after concerns over gatherings where one belief system is said to have been promoted over another, the two said.
The title is the same as the Scottish Parliament's moment of thoughtful tribute set aside for MSPs to quietly consider issues of personal or spiritual importance. The Kirk and humanists' plan will be defended jointly by the usually opposing bodies on Tuesday at the Holyrood petitions committee debate.
Rev Sally Foster Fulton, convenor of the Church of Scotland's Church and Society Council, said the Kirk "welcomes this exciting opportunity to collaborate with our humanist colleagues in supporting genuinely inclusive 'Time for Reflection' in schools that supports the community and spiritual development of all pupils".
She added: "Scotland is a wonderfully diverse nation. Regular, inclusive Time for Reflection will enhance young people's ability to celebrate difference."
Douglas Mclellan, Chief Executive of the Humanist Society Scotland said: "We urge the Public Petitions Committee to make strong recommendation for the change of Religious Observance to 'Time for Reflection'. This removes the exclusivity of Religious Observance and brings about fairness and equality for all.
"If this change is made, it will bring current practices in-line with the modern demographic in Scotland."
Simon Barrow, co-director to Christian think tank Ekklesia said: "It is vital for a healthy society that people of different religious and non-religious outlooks can learn to share public space fairly, collaborate on common values, uphold the rights and dignity of all, and negotiate disagreements with informed respect."