The Church says that some people - including Christians identifying as gay, bisexual or lesbian - would prefer the arrangement over marriage.
Director of mission and public affairs for the CofE, Dr Rev Malcolm Brown was quoted by Christian Today as saying: "We believe that Civil Partnerships still have a place, including for some Christian LGBTI [lesbian, gay, bisexual, transgender and intersex] couples who see them as a way of gaining legal recognition of their relationship."
"Even if the Government's current information-gathering exercise reveals only a small number are taking up Civil Partnerships, we hope it will remain an option."
The Government Equalities Office set out last week plans to consult on whether there was strong enough demand to justify keeping civil partnerships.
While more than 6,300 were typically registered annually in the eight years before the same-sex marriage was legalised in 2014, the figure fell to below 900 in both 2015 and 2016.
In a document released last Friday, the Office said: ""We want to understand why some same-sex couples continue to opt for civil partnership instead of marriage; this is an important part of the evidence base, especially if we decide to phase out or abolish civil partnerships, now that marriage is available to everyone."
Meanwhile, Rebecca Steinfeld and Charles Keidan from west London are currently in a Supreme Court battle as they seek the right to enter into a civil partnership - something heterosexual couples are currently denied.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.