The priests are being urged to ditch the common practice and bless soldiers instead.
Russell Whiting from the Christian Campaign for Nuclear Disarmament told Premier the move represents a "positive step forward".
"We saw just in this country last month with the service at Westminster Abbey, which was seen by many as giving a blessing to nuclear weapons, just what a controversial step it is once clergy members and other Christian leaders get involved," he said.
"Obviously, we want to make sure that all weapons are only used in a severe last resort. And we just don't think it's appropriate that clergy and clerics should be getting involved with blessing them."
In May, the Christian Campaign for Nuclear Disarmament protested outisde Westminster Abbey as they hosted 'A Service to Recognise Fifty Years of Continuous At Sea Deterrent' for the Royal Navy in May.
During the controversial service, the Dean of Westminster praised the use of the UK's nuclear deterrents for bringing peace across the world.
The Moscow Times reported that members of a church council commission met last week in Moscow and discussed and approved the draft revision on the rules covering the blessing of military weapons.
While the new rules state that military hardware may no longer be blessed, they still allow priests to sanctify "personal weapons".
Whiting told Premier he is uncomfortable with the idea of blessing a soldier's mission.
"We have to distinguish between honouring those who serve in our armed forces. And one of the best ways we can do that is actually something that we're not doing enough at the moment, which is looking after them properly once they finish that service.
"I certainly wouldn't have a problem with praying for people before they go, praying for God's protection and his blessing on them while they're in that time period. I'm not sure that I would be happy blessing their mission - that would depend on what the mission was, obviously.
"But really, when you're talking about the weapons, we have to remember certainly weapons of mass destruction and nuclear weapons that we're focused on particularly would kill millions and millions of people if they were ever used.
"And I just don't see how anyone could want to pray a blessing over something that would not only do that, but would also completely change creation as we know it."
A church council commission press release released after last week's meeting listed a number of military situations in which blessings are acceptable.
These include troops being deployed or returning from missions, the opening of new camps and barracks, graduation from military schools and the assignment of new military ranks.
Listen to Premier's Cara Bentley speaking with Russell Whiting:
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