The Ibrox chairman made the claim as he addressed supporters in the announcement of season ticket prices for the 2019/20 campaign.
King insists the club are not far from knocking Celtic off their throne as he backed manager Steven Gerrard to deliver silverware.
Stewart, though, believes it’s a ridiculous comment to make as he feels Rangers still have a long way to go before they can overshadow their rivals.
He said on Monday’s Sportsound: “Every season at this point when Rangers season tickets come out, Dave King comes out with some statement or an announcement to try and push season ticket sales - that’s all this is.
“It’s so transparent it’s actually insult to Rangers fans that are not blinded by this. The majority of them will see this for what it is.
“It’s insulting to their intelligence for him to come out and try and suggest they were within tangible reach of becoming the dominantforce in Scottish football - that is utter, utter rubbish.
“It is not even close, as the season we’ve just seen shows. For Rangers to get to that position, they need Celtic to have another catastrophe of a transfer window like they did last year.
He added: “They need them to financially implode and Rangers to find extra revenue from somewhere and to spend and hit the mark on every acquisition they bring in for them to even stand a remote chance.
“In fact, let’s take it a step further, because that’s what his comments are. He’s not even suggesting they’re within touching distance of stopping nine-in-a-row, he’s saying they’re beyond that.
“That means winning multiple titles and multiple trophies. Can anybody seriously suggest that? I don’t think you can.”