The German was an assistant to former coach Ali Daei, who was fired after a home defeat at the hands of Saudi Arabia in March.
Rutemoeller is no longer active in the national team but feels that Ghotbi, who was appointed two weeks ago, is the right man to resurrect Iran’s qualification campaign with three games remaining.
Iran need at least six points from those games to have a chance.
"I didn't know Ghotbi very well until recently when we had few meetings. I have found him to be a very competent and professional coach. I believe that his great ambition can boost Iran's chances for qualification", Rutemoeller told IRNA.
"Iran's football level is very high. We shouldn't count Iran out of the race yet. Team Melli can still qualify with three wins in the remaining matches.
"I love Iranian football and I hope that Iran will qualify to the World Cup."
The German thinks that Daei should never have been fired in the first place: "Daei's record at the national team was not bad at all. He was sacked by IFF officials only after a single defeat."