It was reported that the Spaniard's future was uncertain at Newcastle because of a lack of involvement in the transfer window.
"I will not leave, I will not quit," Benitez told BBC Newcastle.
"I want to get promoted with this team and to do well. I will put all my effort into that. I say thank you to the fans, I will continue giving everything to ensure the players, staff and fans are pushing in the same direction."
"The window has finished, we have to concentrate on the future," Benitez added. "We have a group of players who did very well in the first part of the season and we have to have confidence they will do well in the second part of the season."
"The club, the city and the fans, we have made the same mistake in the past," Benitez added. "Everyone was blaming each other and we lost the focus.
"We have to stick together and have a target which is promotion and a target to achieve. Afterwards we can analyse the mistakes or what we have done well."