Reports in the local media suggested Baldini, sporting director Walter Sabatini and chief executive Claudio Fenucci were on their way out after a series of indifferent results under coach Zdenek Zeman.
Roma have collected just eight points from a possible 18 with a win over Cagliara awarded to them by the Italian football authorities.
“Nobody is leaving,” said Baldini. “Not me, nor the other directors.
“I’m here at Roma to finish the job that was handed to me by the new owners. But it is work that is being destabilised on a daily basis by false rumours.
“I want to reiterate that neither Fenucci nor Sabatini, nor Mauro Baldissoni or myself have ever had any problems in facing each other. After all, a diversity of opinions is a resource.
“The rumours over the last few days were completely untrue. For as long as I have the strength to continue, I’ll defend the colours of this club and this city.
“We're used to the fact that radio stations slander us on a daily basis, but we would have expected serious news organisations to more accurately check their stories.
“I will say this again, and this is humiliating, that I have had no disagreement with my collaborators with who, over time, I have created a strong friendship with.
“I was chosen to make this a competitive squad. Whether you like it or not, I am staying.”