"The club wants to make it clear that Jose continues to have our full support," read a brief statement on their official website on Monday.
"As Jose has said himself, results have not been good enough and the team's performances must improve. However, we believe that we have the right manager to turn this season around and that he has the squad with which to do it."
Chelsea have already lost six games in all competitions this term and have plunged to fifth from bottom in the league, 10 points behind table-topping Manchester City, after eight matches.
Mourinho, who won the Champions League with Porto in 2004 and Inter Milan six years later, still has the support of most of the fans because of his brilliant record with the club.
In his first spell in charge the self-styled 'Special One' led Chelsea to successive league titles in 2005 and 2006.
After spending time at Inter and Real Madrid, Mourinho rejoined the Stamford Bridge outfit in 2013 and won the Premier League again last season.
He has faced widespread criticism this term for his public spat with former club doctor Eva Carneiro and for the team's poor performances.
"I define this as the worst period in my career," Mourinho said on Friday. "It's a fantastic experience, even though I don't want to repeat it again."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Tony Jimenez)
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