Buyers of the 787 Dreamliner are clamoring for planemaker Boeing Co. to pick up the pace.

So said CEO Jim McNerney on Monday, offering the strongest hint yet that the production rate for the airplane will almost certainly exceed the long-stated goal of 10 jets per month by the end of 2013.

He cited “continued high demand” for the original 787-8 as well as the response to the newer, longer versions of the lightweight, fuel-efficient passenger plane: the 787-9 and 787-10.

“I think the market wants us to,” McNerney said about boosting production. He also said he is “convinced the demand is real and that there is financing for it,” while speaking at the Morgan Stanley Industrials & Autos Conference.

Boeing makes the 787 at plants in North Charleston and Seattle. Any jump in production would put extra demands on one or both sites, and it likely would require more workers.

“The biggest question is the readiness of the supply chain to do it,” McNerney said.

Boeing is making 10 Dreamliners a month right now, he added. “We’re already doing it in our factories ... and our suppliers’ factories ... so we’re pretty much there,” he said.

Most of the 787s are being made in Everett, Wash., where Boeing has set up a temporary “surge line” to speed up the assembly process to help offset several years of delays. The company’s North Charleston factory is projected to turn out three Dreamliners every four weeks by early next year, according to the latest estimate.

Analysts long have speculated that the monthly production rate will have to surpass 10 to fill the more than 800 unfilled orders for the 787. McNerney said the company “will take a disciplined approach” as it decides whether to go higher. “This will minimize the required investment and reduce production risks going forward,” he said.

He also said Boeing wants to ensure the 10-per-month rate becomes “stable” before making a decision. McNerney then quipped that the terms “stable” and “787” haven’t often been used in the same sentence.

For the moment, Boeing is fixed on getting its newly built 787-9 off the ground. The first test flight from Paine Field near Seattle should take place in “the very, very near future,” McNerney said.

Boeing launched an even longer version of the Dreamliner, the 787-10, in June at the Paris Air Show. The company has not said whether either plane will be assembled in North Charleston.