The Argentina captain - who marked his 300th Liga appearance with a hat-trick in Sunday's 5-0 win over Levante - has seen his future become the subject of much discussion in recent months.
An apparent disagreement with coach Luis Enrique, coupled with suggestions from Messi that he did not know where he would be playing next season, fuelled rumours the 27-year-old may leave Camp Nou.
However, Iniesta told FIFA.com: "I hope and wish that Leo can be with Barca for a long time, because he has been, is and will be fundamental to our competing for honours. That's my sole desire."
While Sunday's win extended Barca's winning streak to 11 matches in all competitions, the last few months have been somewhat tumultuous for the Catalan giants.
With a court case ongoing with regards to alleged tax fraud surrounding the signing of Neymar and the club subject to a transfer ban in 2015 for broken rules in relation to the signing of youth players, Iniesta acknowledged it has been difficult to keep focus.
"Look, there's no denying that when there's so much talk on the outside and when it’s not about football or your play, it can affect things," he added.
"You try, or at least should try, to ignore all of that because a lot of it isn't true. The sheer number of reports can annoy you. That said, we know we're at a club where a lot is asked of you, where everything is magnified tenfold.
"There are so many opinions and a lot of things can come from that. When things aren't going exactly to plan, then we have to deal with those kind of situations.
"The only way we can change that and make the public more settled is by playing well and winning.
"That way they forget a bit about all the stuff on the outside and focus instead on what their players are doing on the pitch."
