Amundi, which holds the bond in its Amundi Planet Emerging Green One fund, said it had learnt this week that the Indian bank was considering financing the Carmichael thermal coal mine in Australia.
Carmichael has drawn strong opposition from climate campaigners because of the potential carbon emissions that would be produced by the mine, at a time when many countries are exiting coal to help fight global warming.
Under pressure from investors, a string of banks and insurers have already cut ties to the project, with the most recent being Lloyd's insurer Apollo.
Amundi's Jean Jacques Barberis, Director of the Institutional and Corporate Clients division & ESG, said the asset manager had contacted the bank to voice its concern and followed up with a letter to the management on Thursday.
The Amundi fund - the largest aimed at green bonds in the emerging markets - looks to invest in bonds that help fund environmentally friendly projects, but also looks at the issuer to make sure its other activities are "coherent".
"We consider SBI should not finance this project. It's their decision, ultimately, but we've been extremely clear on the fact that, if they decide to do it, we would immediately disinvest," said Barberis.
Financing the mine would be in "total contradiction" to the SBI activities financed through its green bond, he added. "We have engaged SBI, asking them not to participate (in the loan)... and now we are waiting for their answers."
SBI was not immediately available to comment when contacted by Reuters. The news was reported earlier by Environmental Finance.
(Reporting by Simon Jessop, editing by Louise Heavens)