The Magpies are 19th in the Premier League after three straight defeats.
The club's board met on Monday to discuss the situation, with McClaren expected to take training on Tuesday.
"Someone has to be accountable and decisions must be made," said the statement from the NUFC Fans' Forum.
"What Newcastle fans want is a team of 11 players in black and white shirts that understand their role to perform to their maximum - week in, week out.
"We have entrusted the board of NUFC to ensure that the right personnel are in place to carry out this basic expectation."
Former England manager McClaren took over in the summer, but has only won six of his 28 top-flight matches in charge.
Spanish forward Ayoze Perez insisted on Monday that the players are still behind the 54-year-old - but the squad's effort has also been criticised in the supporters' statement.
"Whilst we have 10 games to go, fans cannot accept the current work ethic of the players," it added.
"Our players frequently look jaded and our playing style often appears outdated. We lack organisation and the players continue to lack discipline."
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McClaren should be sacked as the club embark on a "rescue operation", according to former Newcastle owner Sir John Hall.
And ex-captain Alan Shearer, the Magpies' record goalscorer, says the club is "a mess from top to bottom".
The team were booed off the pitch following the defeat by Bournemouth - their third straight Premier League loss.
"Maybe it's time to accept that the 'head coach' role simply doesn't work at NUFC and accept that a manager is required, a person who will not only coach but motivate and manage," continued the NUFC Fans' Forum letter.
"We must urge you to review our position and initiate any changes that you see fit to correct the current attitude of the playing staff.
"It's time for action, it's time for accountability."
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The supporters' statement also included a number of statistics to illustrate their team's failings under McClaren:
Relegation-threatened Newcastle United have been told it is "time for action and accountability" in a strongly worded letter from fans criticising boss Steve McClaren and his players.