Chelsea cited "sporting integrity" as their reason for asking the clash to be played behind closed doors after they failed to agree an easing in the licence granted last week to continue their operations following owner Roman Abramovich's sanctioning by the U.K. government Thursday.
Middlesbrough issued a strongly worded statement in response to the request, calling it "bizarre, without any merit whatsoever" and "ironic in the extreme."
However, later on Tuesday, the FA said Chelsea have agreed to remove their request, adding that talks are ongoing over a way for the club's fans to attend matches.
English football's governing body said in a statement: "After constructive talks between the FA and Chelsea, the club has agreed to remove their request for the Emirates FA Cup quarterfinal tie against Middlesbrough to be played behind closed doors.
"The FA remains in ongoing discussions with Chelsea, the Premier League and the Government to find a solution that would enable both Chelsea fans to attend games and away fans to attend Stamford Bridge, while ensuring sanctions are respected."
Sources have told ESPN that Chelsea sold around 600 tickets for Saturday's fixture at Riverside Stadium prior to the government's intervention, since when the club have not been allowed to sell tickets as per the terms of their licence.
Chelsea have been in dialogue with the U.K. government aiming to ease the restrictions -- with some success, having had their £500,000 limit on expenditures for staging home games increased to £900,000 -- but previously issued a statement on Tuesday voicing their frustration at a lack of progress elsewhere.
"It is important for the competition that the match against Middlesbrough goes ahead, however it is with extreme reluctance that we are asking the FA board to direct that the game be played behind closed doors for matters of sporting integrity," read the statement.
"Chelsea FC recognises that such an outcome would have a huge impact on Middlesbrough and its supporters, as well as our own fans who have already bought the limited number of tickets that were sold before the licence was imposed, but we believe this is the fairest way of proceeding in the current circumstances."
After the FA confirmed that they will review the application at a board meeting Wednesday, Middlesbrough released their own statement pointing out what they believe is hypocrisy following the government's decision to punish Abramovich -- and by extension Chelsea -- for the 55-year-old's alleged links to Russian president Vladimir Putin following the country's invasion of Ukraine.
"We are aware of Chelsea's request to have Saturday's Emirates FA Cup sixth round tie played behind closed doors and find their suggestion both bizarre and without any merit whatsoever," it read.
"All concerned are well aware of the reasons Chelsea have been sanctioned and that this has nothing to do with Middlesbrough Football Club.
"To suggest as result that MFC and our fans should be penalised is not only grossly unfair but without any foundation.
"Given the reasons for these sanctions, for Chelsea to seek to invoke sporting 'integrity' as reason for the game being played behind closed doors is ironic in the extreme.
"We currently await formal notification from the FA of the next steps but rest assured MFC will resist Chelsea's actions in the strongest terms."
Earlier, Chelsea confirmed they would continue their conversations with the Office of Financial Sanctions Implementation regarding future matches.
"We will continue to discuss the issue of ticket sales with OFSI as there are a number of fixtures still to be played this season and we hope to reach a resolution," the team said in their statement.