Revd Canon David Roper was speaking after the Defence Secretary Michael Fallon made a statement in the House of Commons, saying Britain was not committing any more troops to the island.
However Mr Fallon did commit two Chinook helicopters and £180m of infrastructure investment by 2020 to the Islands.
Prior to his speech, the Sun newspaper reported that Russia was helping Argentina to re-arm with the bombers, increasing the risk of conflict.
Although Britain has ruled the Falkland Islands since 1833, other countries such as Argentina have had settlements there in the past. Both Britain and Argentina claim the islands are theirs.
In 1982, Argentina invaded the Falkland Islands, however British troops defeated them. Around 850 people died in the conflict altogether.
Canon Roper also said it was unlikely the government was making announcements solely based on a report in The Sun, and praised the government for its commitment to the Falkland Islands in terms of defence.
He told Premier's News Hour: "I'm pleased that the British government takes the defence of these islands very seriously. I can't comment on defence of course, but if it [Russia leasing bombers to Argentina] was to happen then of course, it could be a worry for people who live here.
"... to be honest I don't think announcements being made today will have been made on the back of The Sun newspaper.
"I'm here as a pastor, a minister to the whole community, wherever they come from. We have to work for reconciliation and peace between all peoples... but it's not going to be easy."
Listen to Canon Roper speaking to Premier's Antony Bushfield on the News Hour:
