"The conditions are lacking to ensure the necessary serenity to my leading successful productions," Muti said in a letter published by the media, which said he had pulled out of planned productions of Verdi's Aida and Mozart's The Marriage of Figaro.
The 73-year-old said he made the decision to pull out "with the greatest regret, after long and troubled reflection."
The award-winning Muti, who famously quit La Scala in Milan in a dramatic showdown in 2005, was named "honorary director for life" in Rome in 2011.
The Neapolitan native with a trademark mane of dark hair will retain his post as conductor of the Chicago Symphony Orchestra.
The opera house, housed in a 19th-century building near Rome's main railway station that was entirely re-modelled under fascist dictator Benito Mussolini, has vastly expanded its international reach in the past couple of years.
But it has been hit by funding problems as well as management disputes and industrial action which in February and July this year led to mass ticket cancellations and put the house's very future at risk.