Offering manager Arsene Wenger a new contract would be "inappropriate" at the moment, the Arsenal Supporters' Trust has said.
The Frenchman has a year left on his current deal and was linked with Paris St Germain in the summer but dismissed the prospect of a move from the club he joined in October 1996 prior to the end of his existing contract.
Gunners chief executive Ivan Gazidis has stated his intent to retain Wenger beyond the end of the season, but AST wants the club to wait before determining Wenger's future after eight trophyless years and the 3-1 defeat to Aston Villa in their opening Barclays Premier League match on Saturday.
A statement from AST read: "In recent weeks Ivan Gazidis has spoken of the club's intent to offer Arsene Wenger a new contract. The AST believes this is inappropriate.
"A decision on whether to offer an extension to the manager's contract which ends in May 2014 should only be taken following the closing of the transfer window and assessment of the team's performances in the weeks ahead.
"Considerable improvement must be shown for us to be convinced this should happen, and we believe that other senior football appointments must come first.
"The failings we highlighted in Arsene Wenger holding far too much power have only been amplified in recent weeks. These must be addressed as a matter of urgency.
"For now the club's entire focus must be on using the remaining days of the transfer window to strengthen the team significantly."
Some fans took exception to the statement posted on Twitter.
@clockendben wrote: "You do not speak for me as an Arsenal fan. Shambles statement."
@jodal1979 said: "you are not talking on behalf of us all. Why this statement after first game of season? Ridiculous knee jerk attention seeking"
AST claims Wenger has between £70million and £100million to spend, yet Arsenal have struggled to recruit players this summer in another source of frustration for fans.
Majority shareholder Stan Kroenke is culpable, the AST says.
"Stan Kroenke does not attend many Arsenal matches nor does he seem to have the time to devote to the affairs of Arsenal," the statement added.
"But it is clear to all the football personnel he is ultimately responsible for our failing."
There was also fresh criticism of Kroenke from former director Lady Bracewell-Smith, who claimed she "deeply regrets" allowing the American to take control of the club.
Bracewell-Smith, who remains an honorary vice-president, sold her shares in Arsenal to Kroenke in 2011 to help to give him a controlling stake.
Bracewell-Smith has, however, now twice publicly admitted it was a decision she wished she had not made.
"What a shame the board recommended a Kroenke takeover and paid Rothchilds 3m fee," Bracewell-Smith wrote on Twitter. "And how deeply I regret selling to Kroenke. #AFC."
Bracewell-Smith also called on former vice-president David Dein to return and for Russian billionaire Alisher Usmanov, who has a significant stake, to be given a seat on the board.
"Bring David Dein and give Usmanov representation on the board if we are to have success going forward. #AFC," she added.
Bracewell-Smith was equally as forthright in her comments in December - shortly after the Gunners were dumped out of the Capital One Cup by League Two Bradford - claiming Kroenke did not have the best interests of the club at heart.
"Football is a business of passion and SK has no passion for AFC," she wrote at the time. "(Kroenke) shows he cares very little. Why he wanted to be part of AFC I do not know."