The Lord’s prayer would be abolished from the start of Senate sittings and replaced by a statement that includes religious and non-religious beliefs, under a push instigated by the Greens.

On Wednesday the Greens senator Lee Rhiannon will move a motion for a Senate inquiry into the proposed alternative: “Senators, let us in silence pray or reflect upon our responsibilities to all people of Australia and to future generations.”

The move is supported in a letter signed by progressive religious leaders including Fr Rod Bower, of the Anglican parish of Gosford, the reverend Margaret Mayman, of Pitt St Uniting church, and rabbi Jeffrey Kamins of the Temple Emanuel at Woollahra.

Guardian Australia understands the Greens believe they have enough support to set up an inquiry. Senators Stirling Griff and Rex Patrick confirmed Centre Alliance will support the motion, although Patrick noted this is “not the same thing as supporting replacing the prayer”.

Griff suggested the alternative prayer “ensures the moment is more relevant and personal for the individual”.

Senate sittings begin with the Lord’s prayer, a Christian prayer including the words “our father, which art in heaven, hallowed be thy name”.

Rhiannon said the statement that opens parliament “should be inclusive of people of all beliefs and faiths”.

“The Greens are suggesting the proposed new opening statement be referred to the Senate’s procedure committee for a public inquiry that better reflects the secular nature of our country and our parliament,” she said.

“A secular nation like Australia should be free from religious bias and not impose religious influence on citizens or parliamentarians.

“We should work for religious tolerance in the structures of government.”

Mayman said it was “time for the Senate to move on from an opening prayer that belongs to the era when Christianity as the majority religion in Australia was given precedence over other faiths and belief systems”.

“It is time to embrace words that are inclusive and respectful of religious diversity,” she said.

“The archaic language of the current prayer suggests that religious ideas are anachronistic and irrelevant in a pluralistic society.

“The use of the Lord’s prayer is not respectful of Christian faith, as it reduces the prayer that Jesus taught his followers to pray to a rote recitation in this context.”

The letter signed by religious leaders notes the Australian Capital Territory’s legislative assembly begins with a similar non-denominational statement.

“We believe this statement more accurately reflects the multicultural nature of our diverse communities,” it said.

The letter was signed by the Tibetan Buddhist Society of Canberra, the Lebanese Muslim Association at Lakemba and the Quakers at Surry Hills.