The La Liga champions stated that they hoped to avoid a repeat of the "deplorable events" that forced the cancellation of the original fixture on Sunday. A suspected act of sabotage saw the power supply cut at the Estadio de Vallecas ahead of the night's game, leaving the pitch without floodlights.
The decision to reschedule the match was taken shortly after 10pm after it became clear the damage could not be immediately repaired.
But Madrid on Monday expressed misgivings at the decision to stage the rescheduled match under floodlights, citing their busy fixture schedule as a concern should there be any repeat of last night's problems.
"After the deplorable events that took place yesterday, Sunday, and led to the suspension of the Rayo Vallecano-Real Madrid match, Real Madrid C.F. asked the Professional Football League (LFP) to schedule the game today, Monday, during the day in order to avoid any potential problems that might again put it at risk," read a statement on realmadrid.com.
"The president of the LFP has decided, however, that the match will be played at 19:45 and has accepted personal responsibility for it to take place without incident.
"Real Madrid C.F. bases their request on their concern for the lack of dates for the rescheduling of the match should it not be possible for the match to go ahead today."
Vallecano president Raul Martin Presa told the Spanish media on Sunday night the club believed an act of sabotage had taken place.
"Vandals have cut the wire," Presa said in AS. "The police are investigating the incident."
Rayo on Monday morning posted a picture of the severed wiring on their official website, while Cristina Cifuentes, the Government delegate in Madrid, revealed an investigation would be launched to identify the culprits.
Quoted in AS, Cifuentes said it "appears" sabotage was the cause of the outage as there was a "major blight on the lines" that "threatened the lives of people".
She added: "If it was a sabotage, as it seems, it will be investigated to determine those responsible for it."