Parry played down suggestions Benitez was unhappy with the lack of progress being made over funds for new signings and claimed multi-millionaires Tom Hicks and George Gillett are committed to backing the Liverpool coach.
He told BBC Radio Five's Sportsweek programme: "I can reassure Liverpool fans that the commitment of the owners is absolutely clear.
"They are going to provide backing to Rafa, they have made that clear to him this week, so we will be moving forward very positively.
"They have made the point that their commitment is as strong as ever. They think he is the right man for the job, they think he is a fantastic coach, they want to provide him with the backing."
Hicks owns the Dallas Stars ice hockey team and baseball's Texas Rangers, while Gillett owns Montreal Canadiens ice hockey team.
Meanwhile, the row over the choice of the Olympic stadium in Athens to host last Wednesday's Champions League final and the behaviour of Liverpool's fans rumbles on.
Liverpool lost 2-1 to AC Milan in a final that was marred by some Reds supporters using forged and stolen tickets to gain access to the stadium.
Their actions prevented many supporters with valid tickets from watching the game but UEFA insist it was the Greek police who decided to let fans in without tickets.
UEFA's head of communications, William Gaillard, continued to defend the choice of the Olympic stadium and promised to provide Sports Minister Richard Caborn with a report when he and president Michel Platini meet to discuss ground, ticketing and disorder issues on June 5.
Gaillard said: "It is a complicated matter. I think we have to get more information to understand exactly what has been going on, not only in this final, but in the past few seasons.
"We will provide Richard Caborn with a thorough report when we meet him on June 5.
"It is a complex mix of strange fan behaviour, if you can call them fans, because some of them not only had forged tickets but there were some who stole tickets from others. That is criminal behaviour.
"We did our best organising this final the way is should be organised. I don't think we were way off the mark. We had absolutely no problems with the Milan fans for example because they behaved properly.
"What happened at the Liverpool end is a question of public order. It was the behaviour of a few hundred people which caused a lot of trouble. It was the Greek police's decision, not a UEFA decision, because of the threat to the welfare of the other supporters, to let in some of the people without tickets to avoid a very dangerous situation.
"There have been plenty of football matches played in that stadium. It is a modern stadium with all the facilities a modern stadium should have. It is not a stadium dedicated to football but all over Europe there are many stadia that are multi-purpose."
But Gaillard's stance was questioned by Parry, who said he warned UEFA during the days leading up to the final that intelligence suggested 5,000 forged tickets were in existence.
Parry said: "To have a stadium with no counting system and no turnstiles in this day and age, is simply unforgivable for any standard of game, let alone a major final.
"We produced a report for UEFA a week beforehand predicting, sadly, all of the things that did go wrong.
"We told UEFA that our intelligence suggested there were 5,000 forged tickets in existence. They knew and we knew, that thousands of fans would travel without tickets and we stressed the need for a proper check at the outer cordon.
"We do not condone the behaviour of Liverpool fans who charged gates, who stole tickets or who knowingly had forgeries, that is clear. At the same time we are hugely concerned that many innocent fans with valid tickets did not get in. We are concerned that members of our staff were tear-gassed and the checks at the outer cordons did not work."
Caborn hopes UEFA will use the controversy surrounding the choice of the Olympic stadium as a chance to increase the standard of stadia throughout Europe.
Caborn said: "UEFA ought to use this as a wake-up call. I will be discussing this with the president in the next week and asking him how grounds are selected and how we can tackle ticket touts.
"We have learned a lot in England and if UEFA want to get advice from our professionals on ground safety, we'll do that as well.
"I think we can use this to the benefit of lifting the quality of grounds around Europe."