The group that wrote the letter included political satirist Rory Bremner, AC Grayling (writer), Jenni Murray (Radio 4 Woman's Hour), Cristina Odone (journalist), Denis MacShane (MP), Dylan Jones (GQ editor), Mariella Frostrup (presenter), Stephen Frears (director), Helena Kennedy (lawyer and presenter), Alexandra Shulman (Vogue editor), Armando Iannucci (writer of 'The Thick Of It'), Konnie Huq (presenter), Neal Ascherson (journalist) and Neil LaBute (playwright and film director).
Their letter in The Sunday Times called Guardian Media Group's actions "unthinkable" and accused it of stifling a liberal voice.
"We read with alarm that The Guardian is considering closing its sister paper, The Observer.
"It seems unthinkable to us that one liberal newspaper would seek to extinguish another. A pluralist press is vital for a thriving democracy.
"Stifling an elegant voice that has kept millions informed and entertained since the Enlightenment, that has both reported on and helped drive British cultural life, and which is as relevant now as it was when it took principled stands on the American civil war, the Suez crisis and South African apartheid, seems to us to be tragically shortsighted."
The group wrote that while it recognised the intense economic pressure the media was under it said this should not be used as an excuse to close a paper which "offers a unique international perspective".
"The British press is rightly admired for its diversity of opinion, and The Observer has an important place at its core.
"Perhaps a clue to this dangerous proposal lies in Guardian group's aim to turn its website into 'the world's leading liberal voice'. So liberal, in fact, that it can find no room for another point of view."
The letter was also signed by Ben Summerskill, Mark Frankland, David Davis, Peter Kosminsky, Stanley Johnson, Mary Warnock, Marina Warner, Fatima Bhutto, Ed Husain, Nikhil Kumar, Ian Buruma, Samuel West, Aravind Adiga, Jennifer Formichelli, Avi Shlaim, John Gray, Karol Sikora, Colin Byrne, Ronald Harwood, Richard Harries and Anthony Seldon.
Carolyn McCall, the chief executive of Guardian Media Group, is an option as it attempts to reduce debts of close to £90m.
GMG reportedly lost £24m last year on botched currency trading. The investments were made out of a £200m investment fund designed to spread GMG's risk away from volatile advertising markets, according to a report in The Sunday Times.
Two social networking campaigns to save The Observer were launched last week. A has racked up 2,400 followers and a has signed up more than 6,380 supporters.
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