The Spaniard's comments came the day after he criticised the Chelsea board for appointing him only on an interim basis following the sacking of Roberto Di Matteo in November.
"My relationship with the staff and people at the club is really good," the former Liverpool manager, unpopular with Chelsea fans since his appointment, said.
"My relationship with Roman Abramovich is very good. When I meet with Roman Abramovich we talk about football, we talk like normal people and share our passion for football."
Chelsea fans have openly voiced their dissatisfaction with Benitez and the manager earlier this week denied reports of friction with the European champions' senior players following Sunday's 2-0 defeat at Manchester City.
Benitez said he was not worried about being sacked by Russian billionaire Abramovich before his contract runs out at the end of the season.
"The players are really happy in what we are trying to do. Sometimes you win, sometimes you cannot. The atmosphere in the club is really good. There are no issues in the team," the 52-year-old said.
Chelsea became the first Champions League winners to fail to survive the group stages in their title defence when they were eliminated from this season's competition in December.
They are fourth in the Premier League with 11 games left, 19 points behind leaders Manchester United and facing a battle to finish in the top four and earn a Champions League spot next season.
Following Chelsea's 2-0 FA Cup win at Middlesbrough on Wednesday, Benitez hit out at the fans who regularly barrack him at matches and chant Di Matteo's name.
"If we stick together and support the players we will be able to win games," Benitez said. "Then at the end of the season I will leave and then they [the fans] can criticise.
"We still have to play 11 games in the Premier League and we have the FA Cup and the Europa League. Everyone knows I will finish my contract at the end of the season.
"So this group of fans, who are singing and creating banners, they have to concentrate on supporting the team. The rest of the fans, the majority of fans, know the way to help the team is by supporting the players.
Chelsea are through to the Europa League last 16 and play Manchester United in the FA Cup Quarter-Finals next month.
"I'm thinking about my team and my club - I want to win every game," Benitez said. "I tried to explain the way is to support the team in every single game."
Benitez is the 10th Chelsea manager since Abramovich took over the club in 2003.
