He's among dozens of Christian figures urging world leaders to honour previous pledges to tackle the issue.
They've signed a letter calling on world leaders to keep their Paris Agreement promises, ahead of the next round of UN talks on climate.
Greig said: "The real and present crisis of climate change is bigger than political opportunism, bigger than national interest, bigger than us all. Millions of lives are at stake."
The letter, organised by Tearfund as part of the Renew Our World campaign, says: "We urge each nation's leaders to keep the promises they made in the Paris Agreement, to restore the natural balance.
As Christians across the globe, we are calling for action on climate change."
Ben Niblett, senior campaigner for Tearfund told Premier's News Hour the issue should concern everyone.
"We are God's people. We know we are brothers and sisters across the world. So we have the mandate to speak up on behalf Christians in other countries when we hear this is affecting them."
Archbishops across three continents, speaking on behalf of the 85 million-member Anglican Communion, also put their names to the letter, which urges leaders to ensure global warming is limited to 1.5 degrees.
It also asks for more investment in clean off-grid energy that will reach those in poverty who can't access national electricity sources.
The letter continues: "We're committing to respond as Christians by living more sustainably, praying, and raising our voices; we're asking every member of the church - the world's largest network - to join in, alongside many others, and every national leader to lead the way."
Listen to Ben Rogers speaking with Premier's Eno Adeogun here:
