Following a board meeting on Monday, club president Florentino Perez said: "He has all our support and confidence.
"Rafa has only just started his job here. Let him keep working and he will achieve his objectives."
Perez added he could "only talk about this moment".
He said: "I cannot say what will happen in the future. No-one can say what will happen in six months."
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The 68-year-old rejected suggestions striker Cristiano Ronaldo, the Spanish club's record goalscorer, had told him he is unhappy playing under Benitez.
"Ronaldo has never said anything to me about Benitez," he said.
Perez - who returned to the club in 2009 having resigned as president in 2006 - was also a target for angry fans on Saturday.
He said he understood their disappointment but asked them to display "more than ever" their "support to the team and to the players".
Real's next game is at Shakhtar Donetsk in the Champions League on Wednesday, followed by an away game against Eibar in La Liga on Sunday.
The scientists put a new "resistance" gene into the mosquito's own DNA, using a gene editing method called Crispr.
And when the GM mosquitoes mated - their offspring inherited the same resistance, PNAS journal reports.
In theory, if these mosquitoes bite people, they should not be able to pass on the parasite that causes malaria.
About 3.2bn people - almost half of the world's population - are at risk of malaria.
Bed nets, insecticides and repellents can help stop the insects biting and drugs can be given to anyone who catches the infection, but the disease still kills around 580,000 people a year.
Scientists have been searching for new ways to fight malaria.
The University of California team believe their GM mosquito could play a pivotal role - breeding resistant offspring to replace endemic, malaria-carrying mosquitoes.