The move comes after the BBC Trust informed the BBC director-general, Mark Thompson, that annual budget cuts of 3% must be enacted over the next six years.
The cuts are required because of a £2bn funding shortfall resulting from the lower than expected licence fee settlement agreed by the government.
It is understood that news is one of the main areas in line for budget reductions.
The letter expresses the journalists' "dismay" at the cuts being proposed by the management: "We believe the cuts as outlined would make it impossible for us to maintain the editorial standards for which BBC News is famous.
"BBC News is considered by the public to be the most important service the corporation provides. We urge you to safeguard it and reject these proposals."
Next month, the trust will finalise the BBC's six-year strategic investment plan, which will formalise how the BBC will spend the licence fee.
A trust spokesman said: "The chairman has repeatedly made clear that the trust's objective is an efficient BBC delivering quality and distinctive programming which the public values and which the BBC does well."
A BBC spokesman said: "The final decisions about the BBC's plans for the next six years will be taken by the Trust.
"The proposals they are considering are designed to strengthen BBC News in the long term and preserve the quality of our journalism, as well as meeting the financial challenges the BBC faces."
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